P-value Tables

One thing that can be done with trillions of digits is statistical analysis. Many common irrational numbers are conjectured to be normal, meaning their digits are uniformly distributed in every base. Using the y-cruncher output, we can perform statistical analysis on the decimal and hexadecimal digits.

These tables are based on statistics of the first 1 million, 10 million, and so on digits of various real numbers computed to high precision. Each computed digit is treated like a sample and the random variable to compare to is a uniform distribution of the digits.

P values are highlighted in red for below 1%, yellow for below 5%, and green otherwise. The presence of some low P values is expected when computing P values many times because they measure the probability of seeing a measurement at least as extreme.

In each header, there is a hash value. These are the hash values y-cruncher computes, which comes from taking digits of the number as an integer and reducing it modulo 2^61-1, a Mersenne prime. For example, the first 1 million decimal digits after the decimal point in pi, taken as a base 10 integer, reduces to 847519092189756098, modulo 2^61-1. In hexadecimal, the digits should be taken as a hexadecimal integer. These hash values were output from the P value calculator program to make sure (with high probability) it computes statistics on the correct digits.

Pi (decimal)

1 million			10 million			100 million			1 billion			10 billion			100 billion			1 trillion
847519092189756098			1342684684644997977			853340962367853209			1129290375307446070			1047461673576228634			933863534577428190			821983049409748007
digit	count	p	digit	count	p	digit	count	p	digit	count	p	digit	count	p	digit	count	p	digit	count	p
0	99959	0.891294	0	999440	0.554995	0	9999922	0.979257	0	99993942	0.523103	0	999967995	0.286047	0	10000104750	0.269523	0	99999485134	0.086122
1	99758	0.419859	1	999333	0.482006	1	10002475	0.409372	1	99997334	0.778694	1	1000037790	0.207790	1	9999937631	0.510906	1	99999945664	0.856273
2	100026	0.930936	2	1000306	0.747034	2	10001092	0.715858	2	100002410	0.799468	2	1000017271	0.564818	2	10000026432	0.780538	2	100000480057	0.109556
3	100229	0.445265	3	999964	0.969730	3	9998442	0.603528	3	99986911	0.167678	3	999976483	0.433099	3	9999912396	0.355785	3	99999787805	0.479370
4	100230	0.443280	4	1001093	0.249270	4	10003863	0.197862	4	100011958	0.207495	4	999937688	0.037795	4	10000032702	0.730313	4	100000357857	0.232926
5	100359	0.231437	5	1000466	0.623280	5	9993478	0.029705	5	99998885	0.906439	5	1000007928	0.791574	5	9999963661	0.701685	5	99999671008	0.272799
6	99548	0.131896	6	999337	0.484637	6	9999417	0.845915	6	100010387	0.273567	6	999985731	0.634336	6	9999824088	0.063700	6	99999807503	0.521096
7	99800	0.504985	7	1000207	0.827275	7	9999610	0.896566	7	99996061	0.677990	7	1000041330	0.168306	7	10000084530	0.372916	7	99999818723	0.545673
8	99985	0.960122	8	999814	0.844562	8	10002180	0.467430	8	100001839	0.846295	8	999991772	0.783880	8	10000157175	0.097566	8	100000791469	0.008334
9	100106	0.723839	9	1000040	0.966368	9	9999521	0.873144	9	100000273	0.977043	9	1000036012	0.229984	9	9999956635	0.647594	9	99999854780	0.628339

Pi (hexadecimal)

1 million			10 million			100 million			1 billion			10 billion			100 billion			830 billion
498128468367020972			269979704548545667			1881333777557266089			987739783923994387			867911209382615761			1410155165700074604			579126475479587628
digit	count	p	digit	count	p	digit	count	p	digit	count	p	digit	count	p	digit	count	p	digit	count	p
0	62522	0.927583	0	624597	0.598557	0	6250690	0.775605	0	62501979	0.795994	0	625011206	0.643407	0	6249979329	0.787126	0	51874871157	0.559054
1	62385	0.634726	1	624342	0.390005	1	6246592	0.159159	1	62498560	0.850782	1	624994420	0.817688	1	6249991124	0.907688	1	51875089161	0.685988
2	62644	0.551917	2	625896	0.241788	2	6255492	0.023278	2	62508519	0.265744	2	624984447	0.520534	2	6249917131	0.278988	2	51874777165	0.312275
3	62432	0.778771	3	623853	0.134020	3	6250592	0.806793	3	62514233	0.062972	3	624983935	0.506899	3	6250077541	0.311064	3	51875349119	0.113398
4	62235	0.273620	4	623635	0.074549	4	6246996	0.214603	4	62482731	0.024070	4	625014007	0.562822	4	6249925117	0.327942	4	51874867220	0.547108
5	62649	0.538194	5	625491	0.521237	5	6253329	0.169048	5	62501692	0.825060	5	625011152	0.645007	5	6250052283	0.494593	5	51875060941	0.782286
6	62545	0.852521	6	625489	0.522936	6	6251102	0.648925	6	62501242	0.871106	6	624989166	0.654462	6	6250025693	0.737133	6	51875070504	0.749192
7	62515	0.950589	7	625369	0.629764	7	6251231	0.611069	7	62504587	0.549011	7	625010556	0.662773	7	6249958503	0.587740	7	51874815105	0.401796
8	62459	0.865499	8	624959	0.957284	8	6249740	0.914463	8	62495786	0.581966	8	625047187	0.051250	8	6250044644	0.559741	8	51875274249	0.213647
9	62699	0.411017	9	624584	0.586813	9	6246654	0.166882	9	62494524	0.474373	9	624982085	0.459239	9	6249968714	0.682746	9	51875053960	0.806700
a	62070	0.075666	a	625563	0.462035	a	6248822	0.626504	a	62497832	0.777003	a	624987694	0.611185	a	6250055390	0.469304	a	51875187199	0.395956
b	62345	0.521956	b	625077	0.919874	b	6249493	0.834096	b	62489514	0.170723	b	624962532	0.121653	b	6250019064	0.803321	b	51874967447	0.882648
c	62621	0.617164	c	624618	0.617749	c	6250491	0.839259	c	62500734	0.923608	c	625010592	0.661695	c	6250006866	0.928528	c	51875083191	0.705999
d	62829	0.174096	d	626014	0.185276	d	6253342	0.167389	d	62504195	0.583670	d	625010529	0.663583	d	6249933819	0.387267	d	51874815132	0.401865
e	62415	0.725475	e	625462	0.546140	e	6248121	0.437602	e	62501388	0.856110	e	624987488	0.605230	e	6249989678	0.892734	e	51874780196	0.318903
f	62635	0.577043	f	625051	0.946879	f	6247313	0.266978	f	62502484	0.745553	f	625013004	0.591116	f	6250055104	0.471602	f	51874938254	0.779484

e (decimal)

1 million			10 million			100 million			1 billion			10 billion			100 billion			1 trillion
429874372355341578			5381409555245135			1694148922109324462			1959400710726657016			531768131672329868			1174378372379232139			2196705966280381788
digit	count	p	digit	count	p	digit	count	p	digit	count	p	digit	count	p	digit	count	p	digit	count	p
0	99425	0.055280	0	998678	0.163466	0	9999138	0.773857	0	100004425	0.640903	0	1000024802	0.408388	0	9999958528	0.662000	0	100000379385	0.206009
1	100132	0.659937	1	1000577	0.543047	1	10004438	0.139051	1	99982926	0.071899	1	999989229	0.719570	1	10000035626	0.707266	1	100000393071	0.190116
2	99845	0.605389	2	999156	0.373652	2	9998876	0.707908	2	99999168	0.930115	2	999997938	0.945202	2	9999921168	0.405995	2	100000003394	0.990973
3	100228	0.447255	3	1001716	0.070479	3	10005176	0.084467	3	100002498	0.792310	3	999982936	0.569492	3	9999738110	0.005770	3	100000058645	0.845015
4	100389	0.194746	4	1000307	0.746236	4	9998285	0.567548	4	100018922	0.046092	4	1000026506	0.376948	4	10000225617	0.017397	4	100000013702	0.963571
5	100087	0.771816	5	999903	0.918561	5	9998042	0.513971	5	100003884	0.682239	5	999967300	0.275713	5	9999981482	0.845239	5	99999808185	0.522574
6	100479	0.110340	6	998869	0.233191	6	10000158	0.957997	6	99987241	0.178652	6	999931170	0.021771	6	9999872014	0.177308	6	99999441259	0.062537
7	99910	0.764177	7	1000813	0.391457	7	9998342	0.580492	7	99997536	0.795073	7	1000013049	0.663587	7	10000066742	0.481730	7	100000326136	0.276984
8	99814	0.535258	8	999703	0.754231	8	10000336	0.910823	8	100005348	0.572939	8	1000074277	0.013290	8	10000159952	0.091788	8	100000156164	0.602683
9	99691	0.303010	9	1000278	0.769493	9	9997209	0.352199	9	99998052	0.837309	9	999992793	0.810149	9	10000040761	0.667444	9	99999420059	0.053219

e (hexadecimal)

1 million			10 million			100 million			1 billion			10 billion			100 billion			830 billion
2085265759181308585			333917536853471878			872007474554615044			2073606659151287385			2161724429320330129			524760733994700199			996806169034635176
digit	count	p	digit	count	p	digit	count	p	digit	count	p	digit	count	p	digit	count	p	digit	count	p
0	62662	0.503335	0	625524	0.493627	0	6251971	0.415498	0	62502624	0.731750	0	625058205	0.016192	0	6250108428	0.156630	0	51874937135	0.775594
1	62280	0.363424	1	625417	0.585914	1	6257843	0.001195	1	62509363	0.221263	1	625009589	0.692002	1	6250097487	0.202818	1	51875088259	0.688998
2	62224	0.254200	2	624968	0.966654	2	6248763	0.609332	2	62499020	0.898128	2	624956952	0.075340	2	6249999588	0.995706	2	51874637462	0.100186
3	62239	0.280927	3	624042	0.210743	3	6249636	0.880469	3	62504210	0.582325	3	625021657	0.370953	3	6249972865	0.722972	3	51875145499	0.509399
4	62538	0.875257	4	625879	0.250836	4	6248671	0.582982	4	62504055	0.596290	4	624982139	0.460593	4	6249936892	0.409690	4	51874662349	0.125745
5	62449	0.833129	5	624189	0.289379	5	6249714	0.905947	5	62500100	0.989577	5	625014003	0.562934	5	6250053499	0.484610	5	51875294323	0.181999
6	62694	0.422872	6	625192	0.801947	6	6252298	0.342445	6	62499119	0.908371	6	624994621	0.824146	6	6249980579	0.799716	6	51875385537	0.080422
7	62712	0.381133	7	624387	0.423236	7	6246239	0.120247	7	62494135	0.443557	7	624995881	0.864882	7	6250080035	0.295758	7	51875117452	0.594315
8	62185	0.193148	8	625824	0.281718	8	6250436	0.857059	8	62504308	0.573575	8	624978347	0.371041	8	6249844655	0.042416	8	51874829783	0.440198
9	63014	0.033718	9	624233	0.316341	9	6250065	0.978577	9	62500659	0.931394	9	624987309	0.600078	9	6250006907	0.928102	9	51875050576	0.818605
a	62041	0.057932	a	625500	0.513629	a	6247053	0.223429	a	62485845	0.064429	a	625019933	0.410242	a	6249966116	0.658013	a	51874809399	0.387428
b	62382	0.625919	b	626132	0.139183	b	6252484	0.304804	b	62497284	0.722727	b	624999955	0.998517	b	6249871327	0.092767	b	51874473936	0.017057
c	62669	0.485071	c	624741	0.735095	c	6249873	0.958157	c	62494093	0.440300	c	625015832	0.513080	c	6250087061	0.255388	c	51875073072	0.740381
d	62962	0.056313	d	624330	0.381419	d	6246093	0.106516	d	62504269	0.577049	d	625011021	0.648895	d	6250026173	0.732409	d	51875153146	0.487400
e	62366	0.579867	e	624096	0.237610	e	6248349	0.495202	e	62502039	0.789951	e	624982328	0.465352	e	6249895943	0.174021	e	51875023577	0.914859
f	62583	0.731683	f	625546	0.475665	f	6250512	0.832484	f	62498877	0.883362	f	624972228	0.251253	f	6250072445	0.343936	f	51875318495	0.148673

Golden Ratio (decimal)

1 million			10 million			100 million			1 billion			10 billion			100 billion			1 trillion
944312423434632608			1315679001245085414			1260810752112751175			601316853453783121			1440137552239732345			1201247783343915658			779847117051622152
digit	count	p	digit	count	p	digit	count	p	digit	count	p	digit	count	p	digit	count	p	digit	count	p
0	99805	0.515692	0	1001143	0.228270	0	10003332	0.266712	0	100007840	0.408572	0	1000031042	0.300793	0	10000052724	0.578375	0	99999918136	0.784945
1	99993	0.981384	1	1000118	0.901012	1	10000255	0.932261	1	99999864	0.988562	1	999990982	0.763720	1	10000040074	0.672721	1	100000717905	0.016710
2	99529	0.116415	2	1000776	0.413371	2	10002116	0.480603	2	100002106	0.824320	2	1000005392	0.857362	2	9999960844	0.679797	2	99999281477	0.016617
3	99833	0.577755	3	999794	0.828097	3	9999184	0.785622	3	99979352	0.029519	3	999978183	0.467083	3	9999881095	0.210072	3	99999995716	0.988607
4	100151	0.614730	4	999367	0.504618	4	9998797	0.688420	4	99995481	0.633829	4	999952470	0.113118	4	10000032055	0.735447	4	100000431112	0.150707
5	100067	0.823276	5	999725	0.771912	5	9996151	0.199492	5	99999934	0.994449	5	1000032985	0.271550	5	9999833743	0.079687	5	100000267801	0.372034
6	100328	0.274247	6	999455	0.565643	6	9996149	0.199259	6	100004208	0.657359	6	1000014191	0.636189	6	10000019716	0.835366	6	99999951791	0.872332
7	100160	0.593803	7	1000852	0.369139	7	9997524	0.409182	7	100018237	0.054562	7	1000023870	0.426226	7	10000150955	0.111563	7	99999541575	0.126492
8	100236	0.431477	8	1000059	0.950410	8	10005419	0.070866	8	99995223	0.614585	8	999976728	0.437906	8	10000068382	0.471027	8	100000040075	0.893732
9	99898	0.733857	9	998711	0.174234	9	10001073	0.720593	9	99997755	0.812933	9	999994157	0.845576	9	9999960412	0.676463	9	99999854412	0.627468

Golden Ratio (hexadeceimal)

1 million			10 million			100 million			1 billion			10 billion			100 billion			830 billion
1919782923793360354			358973849997484651			1374207286213649354			1442086360959447624			1688274149165336465			339957470715658246			2167612526587835808
digit	count	p	digit	count	p	digit	count	p	digit	count	p	digit	count	p	digit	count	p	digit	count	p
0	62447	0.826687	0	623289	0.025402	0	6245058	0.041188	0	62494497	0.472197	0	625034491	0.154190	0	6250110837	0.147626	0	51874901987	0.656720
1	62377	0.611358	1	625136	0.858982	1	6251277	0.597810	1	62497101	0.704893	1	624986241	0.569757	1	6249901207	0.196833	1	51874416689	0.008168
2	61985	0.033374	2	623397	0.036247	2	6248680	0.585536	2	62496653	0.661930	2	624989629	0.668327	2	6250018029	0.813797	2	51875174158	0.429685
3	62669	0.485071	3	622781	0.003745	3	6241305	0.000328	3	62491239	0.252403	3	625004072	0.866409	3	6250047695	0.533229	3	51875239509	0.277449
4	62721	0.361247	4	625309	0.686451	4	6245259	0.050160	4	62504143	0.588343	4	625011110	0.646253	4	6249858545	0.064608	4	51874613766	0.079877
5	62913	0.087975	5	626309	0.087253	5	6254732	0.050598	5	62505236	0.493957	5	625012199	0.614287	5	6250114539	0.134567	5	51875108444	0.622899
6	62214	0.237397	6	626275	0.095783	6	6249135	0.720832	6	62496233	0.622635	6	624961079	0.107858	6	6250032155	0.674433	6	51875119072	0.589239
7	62393	0.658463	7	625443	0.562769	7	6252756	0.254889	7	62506679	0.382913	7	624993741	0.795966	7	6249955089	0.557395	7	51874907493	0.674866
8	62536	0.881773	8	625839	0.273050	8	6247958	0.398900	8	62505241	0.493545	8	625017046	0.481307	8	6249981169	0.805677	8	51874992322	0.972226
9	62932	0.074315	9	626065	0.164131	9	6252546	0.292892	9	62501125	0.883156	9	625040580	0.093653	9	6249979973	0.793605	9	51874887257	0.609183
a	62674	0.472248	a	625480	0.530614	a	6251541	0.524376	a	62514022	0.066977	a	624997459	0.916397	a	6250020430	0.789549	a	51875154314	0.484086
b	62298	0.404000	b	625124	0.871311	b	6254901	0.042899	b	62491678	0.276957	b	624996257	0.877113	b	6250011021	0.885518	b	51875166991	0.448911
c	62531	0.898096	c	624527	0.536625	c	6254539	0.060773	c	62510477	0.171090	c	625026265	0.277897	c	6249910598	0.242830	c	51874847954	0.490533
d	62519	0.937436	d	624939	0.936484	d	6251930	0.425266	d	62504011	0.600282	d	624988571	0.636818	d	6250147006	0.054798	d	51875184424	0.402996
e	62089	0.089524	e	623643	0.076266	e	6247948	0.396595	e	62489145	0.156164	e	624941569	0.015783	e	6249992123	0.918039	e	51875167848	0.446587
f	62702	0.404000	f	626444	0.059237	f	6250435	0.857383	f	62492520	0.328479	f	624999691	0.989815	f	6249919584	0.293465	f	51875117772	0.593311

Zeta(3) (decimal)

1 million			10 million			100 million			1 billion			10 billion			100 billion			1 trillion
2137085247805661829			190615168839065143			423423689230144796			1920392548940788160			1884867502882333131			1571537840618934580			554561106555940252
digit	count	p	digit	count	p	digit	count	p	digit	count	p	digit	count	p	digit	count	p	digit	count	p
0	99761	0.425645	0	1000416	0.661022	0	9999248	0.802072	0	100001073	0.909948	0	1000013285	0.657886	0	9999974826	0.790734	0	100000022438	0.940379
1	100273	0.362823	1	1000484	0.609925	1	10000163	0.956670	1	99996430	0.706686	1	1000020953	0.484906	1	9999968186	0.737362	1	100000160787	0.591988
2	100012	0.968093	2	1001036	0.274816	2	10005579	0.062933	2	99985752	0.133130	2	999958136	0.162875	2	9999913021	0.359227	2	99999702782	0.321819
3	99894	0.723839	3	998032	0.038037	3	10000695	0.816797	3	100007728	0.415300	3	999986237	0.646402	3	10000016952	0.858181	3	100000228651	0.445959
4	99904	0.748968	4	998174	0.054258	4	9991603	0.005126	4	99994148	0.537330	4	999978725	0.478221	4	10000056037	0.554734	4	100000103582	0.729889
5	100399	0.183518	5	1002043	0.031279	5	10003610	0.228847	5	99999279	0.939419	5	999960574	0.188779	5	10000034951	0.712563	5	100000264772	0.377467
6	99525	0.113346	6	999818	0.847864	6	10003630	0.226279	6	100014221	0.133867	6	1000020812	0.487849	6	10000043022	0.650195	6	99999711143	0.335619
7	100616	0.040040	7	1000198	0.834674	7	9995077	0.100797	7	99993290	0.479382	7	1000016369	0.585318	7	10000056326	0.552694	7	99999981422	0.950621
8	99675	0.278660	8	999969	0.973932	8	10001192	0.691122	8	100009336	0.325066	8	1000035324	0.239009	8	10000044998	0.635271	8	100000147357	0.623292
9	99941	0.844088	9	999830	0.857784	9	9999203	0.790496	9	99998743	0.894589	9	1000009585	0.749347	9	9999891681	0.253544	9	99999677066	0.281728

Zeta(3) (hexadecimal)

1 million			10 million			100 million			1 billion			10 billion			100 billion			830 billion
2211762355535330252			686637540253762283			1842902514352442455			310503552139465461			1895984559412745665			1006173770163985494			619287144184347509
digit	count	p	digit	count	p	digit	count	p	digit	count	p	digit	count	p	digit	count	p	digit	count	p
0	62110	0.107145	0	624521	0.531470	0	6249720	0.907912	0	62504756	0.534388	0	625013588	0.574562	0	6250029114	0.703690	0	51874855444	0.512147
1	62666	0.492854	1	625130	0.865143	1	6248842	0.632372	1	62505192	0.497594	1	624980482	0.420056	1	6250039530	0.605563	1	51875252801	0.251654
2	62726	0.350486	2	625649	0.396521	2	6253540	0.143621	2	62502303	0.763519	2	625001913	0.937009	2	6249970944	0.704253	2	51874898670	0.645884
3	62416	0.728577	3	625204	0.789851	3	6253480	0.150533	3	62509779	0.201418	3	625020802	0.390137	3	6250057138	0.455397	3	51874801539	0.368156
4	62621	0.617164	4	624130	0.255721	4	6248755	0.607020	4	62513390	0.080246	4	625013028	0.590432	4	6249985208	0.846770	4	51875240865	0.274738
5	62643	0.554682	5	623164	0.016461	5	6248956	0.666254	5	62495006	0.514135	5	625011588	0.632137	5	6250097967	0.200603	5	51875444487	0.043847
6	62113	0.109872	6	624573	0.576960	6	6246709	0.173965	6	62492075	0.300521	6	624980351	0.416943	6	6250061972	0.418171	6	51874868288	0.550336
7	62423	0.750408	7	625432	0.572507	7	6247149	0.238876	7	62489619	0.175046	7	624975542	0.312302	7	6250010184	0.894159	7	51875321745	0.144573
8	63068	0.018950	8	627100	0.006080	8	6252056	0.395675	8	62483609	0.032249	8	624981280	0.439311	8	6249944324	0.467013	8	51875202343	0.358861
9	62817	0.190336	9	626034	0.176756	9	6250033	0.989123	9	62506087	0.426496	9	625080961	0.000824	9	6250006022	0.937294	9	51875041028	0.852410
a	62686	0.442250	a	625858	0.262336	a	6247572	0.315836	a	62498167	0.810747	a	624965189	0.150404	a	6249967625	0.672335	a	51875006520	0.976414
b	62286	0.376657	b	624122	0.251376	b	6250228	0.924957	b	62495857	0.588343	b	625003143	0.896691	b	6250219087	0.004208	b	51875272951	0.215822
c	62553	0.826687	c	625391	0.609491	c	6251733	0.474032	c	62498210	0.815106	c	624984398	0.519221	c	6249956196	0.567151	c	51874679763	0.146464
d	62498	0.993408	d	624116	0.248151	d	6251349	0.577325	d	62489929	0.188285	d	624955879	0.068346	d	6249882413	0.124502	d	51874515469	0.028011
e	62299	0.406331	e	625776	0.310696	e	6250506	0.834419	e	62502571	0.736966	e	624999720	0.990771	e	6249922376	0.310547	e	51874603597	0.072254
f	62075	0.079131	f	623800	0.116957	f	6249372	0.795297	f	62513450	0.078901	f	625032136	0.184311	f	6249849900	0.049891	f	51874994490	0.980067

Lemniscate (decimal)

1 million			10 million			100 million			1 billion			10 billion			100 billion			1 trillion
30689010460973544			1106426702819548304			675074360569078103			765151707132328113			403300822484754745			983315492474161690			698230824284215074
digit	count	p	digit	count	p	digit	count	p	digit	count	p	digit	count	p	digit	count	p	digit	count	p
0	100104	0.728842	0	999417	0.538861	0	9999619	0.898940	0	100001277	0.892922	0	1000024984	0.404958	0	10000044587	0.638363	0	100000089155	0.766327
1	100289	0.335380	1	1001369	0.149006	1	10001676	0.576389	1	100014939	0.115324	1	1000052218	0.081754	1	10000222543	0.018986	1	100000106321	0.723037
2	100222	0.459300	2	1000174	0.854475	2	10000434	0.884974	2	99997354	0.780312	2	999963501	0.223744	2	9999983003	0.857809	2	99999532169	0.118893
3	100233	0.437355	3	999397	0.525026	3	9998976	0.732853	3	99996759	0.732628	3	1000008919	0.766237	3	9999901688	0.300062	3	100000103354	0.730460
4	99818	0.544072	4	999623	0.691078	4	9998242	0.557876	4	99985891	0.136957	4	999956380	0.145946	4	9999955478	0.638853	4	99999767295	0.437936
5	100226	0.451250	5	1001295	0.172237	5	10004897	0.102609	5	100010796	0.255121	5	1000062533	0.037121	5	9999925577	0.432754	5	100000184166	0.539290
6	100020	0.946847	6	1000689	0.467673	6	10004589	0.126099	6	100005949	0.530607	6	1000024780	0.408804	6	9999990416	0.919531	6	100000571768	0.056664
7	99635	0.223731	7	1000081	0.931958	7	10000124	0.967030	7	99997848	0.820548	7	999969107	0.303120	7	9999963843	0.703108	7	99999785854	0.475338
8	99722	0.354100	8	999156	0.373652	8	9991654	0.005403	8	99979589	0.031436	8	999956634	0.148308	8	9999973960	0.783711	8	99999617336	0.202116
9	99731	0.369897	9	998799	0.205526	9	9999789	0.943928	9	100009598	0.311673	9	999980944	0.525298	9	10000038905	0.681736	9	100000242582	0.418741

Lemniscate (hexadecimal)

1 million			10 million			100 million			1 billion			10 billion			100 billion			830 billion
2089909640619388043			973823582457026155			274679096863124264			353134896252600689			1605059776801706919			2099456727544731961			565056842105346057
digit	count	p	digit	count	p	digit	count	p	digit	count	p	digit	count	p	digit	count	p	digit	count	p
0	62478	0.927583	0	625254	0.740022	0	6250963	0.690753	0	62499407	0.938250	0	624997247	0.909451	0	6250032984	0.666540	0	51875138553	0.529822
1	62180	0.186175	1	625303	0.692225	1	6249073	0.701749	1	62503960	0.604924	1	625039989	0.098531	1	6250149757	0.050416	1	51875304333	0.167581
2	62471	0.904638	2	625218	0.775802	2	6251008	0.677100	2	62518292	0.016864	2	625013438	0.578793	2	6250001227	0.987211	2	51875343490	0.119334
3	62685	0.444707	3	625753	0.325256	3	6251389	0.566089	3	62500485	0.949480	3	625002764	0.909090	3	6250070839	0.354739	3	51874825724	0.429373
4	62234	0.271814	4	624646	0.643749	4	6247729	0.348146	4	62505271	0.491075	4	625010904	0.652376	4	6249921780	0.306846	4	51874899704	0.649254
5	62592	0.703894	5	625427	0.576960	5	6251671	0.489993	5	62494623	0.482400	5	625057893	0.016772	5	6250145597	0.057162	5	51875226464	0.304461
6	62520	0.934151	6	624157	0.270770	6	6248641	0.574506	6	62505007	0.513040	6	625020249	0.402861	6	6250038138	0.618320	6	51874975968	0.913223
7	62646	0.546407	7	624441	0.465222	7	6250760	0.753544	7	62495433	0.550754	7	625002637	0.913251	7	6250046927	0.539842	7	51874721929	0.207334
8	62601	0.676496	8	623781	0.111274	8	6247930	0.392465	8	62490062	0.194186	8	624979132	0.388635	8	6250011508	0.880496	8	51875009562	0.965415
9	62130	0.126379	9	624698	0.693189	9	6244694	0.028379	9	62502495	0.744466	9	624992913	0.769693	9	6249876008	0.105270	9	51874817278	0.407351
a	62695	0.420485	a	624600	0.601282	a	6251285	0.595518	a	62488567	0.135280	a	624986980	0.590660	a	6249947717	0.494593	a	51874862000	0.531466
b	62412	0.716199	b	624028	0.204150	b	6252806	0.246371	b	62510429	0.173059	b	624964596	0.143576	b	6249916613	0.275994	b	51874796987	0.357272
c	62906	0.093492	c	626202	0.116349	c	6249522	0.843459	c	62504576	0.549969	c	624976551	0.332684	c	6249867550	0.083573	c	51874937524	0.776946
d	62492	0.973635	d	625068	0.929213	d	6246364	0.133072	d	62488249	0.124748	d	624995390	0.848958	d	6249932795	0.379964	d	51874729861	0.220590
e	62733	0.335766	e	625480	0.530614	e	6253334	0.168408	e	62488501	0.133040	e	624967381	0.177803	e	6249979390	0.787739	e	51875197119	0.371403
f	62225	0.255925	f	625944	0.217488	f	6252831	0.242187	f	62504643	0.544144	f	624991936	0.739030	f	6250061170	0.424220	f	51875213504	0.332971

Catalan (decimal)

1 million			10 million			100 million			1 billion			10 billion			100 billion			1 trillion
609146920609449948			1991658500209565645			2166768102884349819			1406649325839505883			1327416867237860080			1199526426282890554			1722077503573289556
digit	count	p	digit	count	p	digit	count	p	digit	count	p	digit	count	p	digit	count	p	digit	count	p
0	99620	0.205275	0	999784	0.819892	0	9998686	0.661386	0	99996067	0.678453	0	999968924	0.300264	0	9999865357	0.155823	0	100000315690	0.292662
1	99697	0.312495	1	1000293	0.757436	1	10003813	0.203729	1	100006305	0.506303	1	1000004905	0.870125	1	10000172070	0.069712	1	100000172385	0.565551
2	100168	0.575479	2	1001789	0.059326	2	10005122	0.087760	2	100000806	0.932293	2	999982215	0.553293	2	10000047634	0.615593	2	100000412213	0.169428
3	99580	0.161513	3	999672	0.729536	3	9995676	0.149491	3	100001483	0.875779	3	999978599	0.475619	3	10000042296	0.655714	3	99999531785	0.118591
4	100074	0.805166	4	1000165	0.861924	4	9995377	0.123317	4	100001871	0.843655	4	1000006862	0.819076	4	10000078825	0.406037	4	99999833922	0.579857
5	100053	0.859770	5	999965	0.970570	5	9999309	0.817833	5	100000777	0.934724	5	999996781	0.914551	5	10000048972	0.605708	5	99999317679	0.022942
6	100201	0.502858	6	998712	0.174568	6	10000674	0.822239	6	99998816	0.900678	6	1000028667	0.339291	6	9999875334	0.188814	6	100000307743	0.304981
7	100083	0.782036	7	1000510	0.590862	7	10003863	0.197862	7	100000576	0.951586	7	1000005699	0.849335	7	10000046308	0.625458	7	100000024454	0.935034
8	100352	0.240662	8	999298	0.459316	8	9997437	0.392920	8	100000863	0.927518	8	1000022451	0.454239	8	9999983182	0.859291	8	100000219841	0.463678
9	100172	0.566419	9	999812	0.842913	9	10000043	0.988564	9	99992436	0.425268	9	1000004897	0.870335	9	9999840022	0.091735	9	99999864288	0.651000

Catalan (hexadecimal)

1 million			10 million			100 million			1 billion			10 billion			100 billion			830 billion
1688164286555059983			770661630225251504			1228365388073566791			1549581109747252206			1107288465641773252			528461785757965820			811658931329759142
digit	count	p	digit	count	p	digit	count	p	digit	count	p	digit	count	p	digit	count	p	digit	count	p
0	62328	0.477355	0	624934	0.931290	0	6251309	0.588665	0	62494289	0.455618	0	624980876	0.429500	0	6250053285	0.486358	0	51875221288	0.315647
1	62427	0.762975	1	624471	0.489514	1	6249610	0.872002	1	62494734	0.491486	1	624999838	0.994660	1	6250028923	0.705543	1	51875208124	0.345297
2	62605	0.664452	2	625695	0.363908	2	6249019	0.685280	2	62485109	0.051733	2	625001524	0.949799	2	6249885127	0.133435	2	51874724917	0.212258
3	62917	0.084942	3	626461	0.056308	3	6251842	0.446679	3	62509686	0.205737	3	624992175	0.746495	3	6249925909	0.333084	3	51875140576	0.523831
4	61997	0.037711	4	623535	0.055637	4	6248860	0.637673	4	62502726	0.721748	4	624988015	0.620514	4	6250082486	0.281216	4	51875361117	0.101525
5	62737	0.327535	5	625213	0.780811	5	6247548	0.311076	5	62507161	0.349526	5	624971859	0.245010	5	6249822169	0.020170	5	51874994660	0.980681
6	62519	0.937436	6	624278	0.345570	6	6246773	0.182488	6	62480726	0.011804	6	624997228	0.908828	6	6250013763	0.857310	6	51874684407	0.152408
7	62183	0.190336	7	625445	0.561008	7	6254633	0.055623	7	62505198	0.497097	7	625061074	0.011633	7	6250139611	0.068172	7	51875137669	0.532451
8	62760	0.282775	8	625780	0.308209	8	6248988	0.675892	8	62503564	0.641503	8	624979599	0.399339	8	6249929502	0.357060	8	51875034503	0.875674
9	62301	0.411017	9	625118	0.877488	9	6250447	0.853493	9	62510807	0.158003	9	624978916	0.383744	9	6250002889	0.969894	9	51874952056	0.827893
a	62174	0.178056	a	624170	0.278228	a	6250352	0.884381	a	62494495	0.472036	a	625010877	0.653180	a	6250042210	0.581340	a	51874855764	0.513082
b	62786	0.237397	b	625019	0.980197	b	6253019	0.212323	b	62521091	0.005864	b	625013127	0.587612	b	6249998475	0.984105	b	51875062898	0.775480
c	62522	0.927583	c	625411	0.591317	c	6251900	0.432498	c	62486597	0.079953	c	624978401	0.372235	c	6250036564	0.632885	c	51874760849	0.278168
d	62717	0.370004	d	624441	0.465222	d	6247550	0.311471	d	62495150	0.526341	d	625018913	0.434608	d	6249901257	0.197060	d	51874688013	0.157149
e	62182	0.188942	e	625079	0.917800	e	6248500	0.535470	e	62502747	0.719695	e	625013796	0.568720	e	6250024438	0.749532	e	51874866999	0.546441
f	62845	0.154083	f	624950	0.947919	f	6249650	0.885034	f	62505920	0.439294	f	625013782	0.569112	f	6250113392	0.138514	f	51875306160	0.165045

Log(2) (decimal)

1 million			10 million			100 million			1 billion			10 billion			100 billion			1 trillion
2137329331986983984			1498844399084650316			1407731008274555667			1316624018824653949			1830971725130095921			2151275494591098329			2254138001579091940
digit	count	p	digit	count	p	digit	count	p	digit	count	p	digit	count	p	digit	count	p	digit	count	p
0	100154	0.607718	0	1000511	0.590134	0	10001186	0.692597	0	100001802	0.849350	0	999978838	0.480561	0	9999973563	0.780498	0	99999928448	0.811488
1	100301	0.315700	1	1001157	0.222622	1	10001248	0.677410	1	99998638	0.885842	1	1000029327	0.328289	1	9999785331	0.023647	1	100000059310	0.843280
2	99496	0.092957	2	998535	0.122529	2	10002102	0.483511	2	100026184	0.005780	2	1000058738	0.050238	2	9999862179	0.146290	2	99999703208	0.322513
3	99995	0.986703	3	999427	0.545847	3	9995171	0.107471	3	99992387	0.422275	3	999973190	0.371500	3	9999956236	0.644574	3	100000025944	0.931085
4	99735	0.377056	4	1000673	0.478074	4	9999885	0.969422	4	99976028	0.011508	4	999922371	0.009664	4	9999986374	0.885792	4	99999808895	0.524114
5	100222	0.459300	5	998290	0.071467	5	9998600	0.640738	5	99991321	0.360272	5	999950147	0.096560	5	10000083253	0.380181	5	100000108493	0.717619
6	99864	0.650309	6	999325	0.476767	6	9995182	0.108274	6	99999116	0.925759	6	999997340	0.929347	6	10000084075	0.375495	6	100000027886	0.925941
7	99857	0.633600	7	1001103	0.244966	7	10004947	0.099148	7	100002793	0.768446	7	1000050065	0.095150	7	10000139329	0.141926	7	100000321136	0.284415
8	99832	0.575479	8	1000757	0.424901	8	9998730	0.672052	8	100003765	0.691466	8	1000012121	0.686188	8	10000045205	0.633716	8	99999883793	0.698492
9	100544	0.069780	9	1000222	0.814978	9	10002949	0.325607	9	100007966	0.401082	9	1000027863	0.353010	9	10000084455	0.373340	9	100000132887	0.657797

Log(2) (hexadecimal)

1 million			10 million			100 million			1 billion			10 billion			100 billion			830 billion
737050780120810646			968226290430679914			16184583146907825			594947315377588055			2036611841775674167			1407437111459140849			92618444764672017
digit	count	p	digit	count	p	digit	count	p	digit	count	p	digit	count	p	digit	count	p	digit	count	p
0	62345	0.521956	0	625536	0.483785	0	6250410	0.865499	0	62508612	0.260561	0	625008500	0.725475	0	6250022359	0.770213	0	51875068414	0.756388
1	62478	0.927583	1	624251	0.327832	1	6247584	0.318234	1	62507076	0.355276	1	625021379	0.377125	1	6250059365	0.438020	1	51875125985	0.567805
2	62472	0.907912	2	624370	0.410492	2	6244601	0.025719	2	62502579	0.736178	2	624964345	0.140758	2	6250028684	0.707864	2	51875166987	0.448922
3	62581	0.737907	3	625243	0.750899	3	6252835	0.241522	3	62492281	0.313260	3	624985447	0.547699	3	6250051161	0.503901	3	51874975253	0.910652
4	62795	0.222959	4	624360	0.403103	4	6250365	0.880143	4	62510126	0.185884	4	624994211	0.810986	4	6250031810	0.677729	4	51874929037	0.747615
5	62688	0.437358	5	626129	0.140234	5	6249970	0.990112	5	62504639	0.544491	5	625015106	0.532591	5	6249927812	0.345650	5	51875102177	0.643129
6	62427	0.762975	6	623895	0.148861	6	6248471	0.527611	6	62489553	0.172319	6	624979666	0.400889	6	6249793056	0.006861	6	51874666619	0.130601
7	62547	0.846046	7	625245	0.748918	7	6246755	0.180061	7	62499065	0.902782	7	625028864	0.233095	7	6250093966	0.219610	7	51875218162	0.322532
8	62306	0.422872	8	624774	0.767807	8	6248964	0.668658	8	62502914	0.703438	8	624971496	0.238975	8	6249927737	0.345149	8	51874867900	0.549162
9	62769	0.266444	9	625417	0.585914	9	6250078	0.974294	9	62485787	0.063343	9	624971946	0.246472	9	6249961828	0.618007	9	51875353123	0.109320
a	62238	0.279088	a	626282	0.093974	a	6253389	0.161496	a	62504470	0.559248	a	625053042	0.028433	a	6250025953	0.734573	a	51875029662	0.893004
b	62307	0.425266	b	624088	0.233484	b	6248255	0.470976	b	62499496	0.947503	b	625012967	0.592173	b	6249936085	0.403728	b	51874936113	0.772046
c	62668	0.487658	c	625572	0.454908	c	6250803	0.740090	c	62511725	0.125585	c	625019061	0.431022	c	6249967693	0.672984	c	51874441990	0.011396
d	62507	0.976930	d	625171	0.823229	d	6254183	0.083975	d	62491912	0.290689	d	624970708	0.226238	d	6249948303	0.499443	d	51874851037	0.499370
e	62549	0.839582	e	624431	0.457277	e	6251256	0.603847	e	62477410	0.003166	e	624979665	0.400866	e	6250128259	0.093823	e	51875022656	0.918173
f	62323	0.464645	f	625236	0.757847	f	6252081	0.389955	f	62512355	0.106516	f	625023597	0.329642	f	6250095929	0.210129	f	51875244885	0.266807

Log(3) (decimal)

1 million			10 million			100 million			1 billion			10 billion			100 billion			1 trillion
1588012098981075861			1414116006235552428			889948522285119018			1158632287081373225			1420059175048227268			2144871018234980370			417568512167836925
digit	count	p	digit	count	p	digit	count	p	digit	count	p	digit	count	p	digit	count	p	digit	count	p
0	100214	0.475640	0	999861	0.883512	0	9997237	0.357050	0	100004262	0.653248	0	999999871	0.996569	0	10000013576	0.886208	0	99999659518	0.256400
1	100182	0.544072	1	1000597	0.529157	1	9993564	0.031926	1	99991259	0.356851	1	999950818	0.101130	1	9999824494	0.064314	1	99999589492	0.171199
2	99924	0.800011	2	998944	0.265656	2	10000530	0.859770	2	99996348	0.700271	2	999950111	0.096319	2	9999906211	0.322848	2	100000178634	0.551545
3	99668	0.268438	3	999016	0.299630	3	10000437	0.884185	3	100004916	0.604324	3	1000008395	0.779605	3	9999948649	0.588310	3	100000092833	0.756984
4	100250	0.404657	4	999915	0.928607	4	10000525	0.861080	4	100000531	0.955364	4	999989238	0.719795	4	9999952438	0.616127	4	100000175944	0.557553
5	100071	0.812915	5	1000321	0.735089	5	10003926	0.190647	5	99998498	0.874201	5	999995761	0.887633	5	10000057599	0.543754	5	99999928890	0.812631
6	99727	0.362823	6	1000184	0.846213	6	10004196	0.161913	6	99991864	0.391108	6	1000062530	0.037130	6	10000038492	0.684933	6	100000337267	0.260918
7	100452	0.131896	7	1001522	0.108642	7	9996941	0.307887	7	100002604	0.783711	7	1000047537	0.113065	7	10000100222	0.290771	7	100000143002	0.633595
8	99603	0.185725	8	999928	0.939503	8	10001717	0.567096	8	100006004	0.526814	8	999994412	0.852236	8	10000016245	0.864037	8	99999892244	0.719455
9	99909	0.761636	9	999712	0.761449	9	10000927	0.757322	9	100003714	0.695435	9	1000001327	0.964718	9	10000142074	0.134239	9	100000002176	0.994213

Log(3) (hexadecimal)

1 million			10 million			100 million			1 billion			10 billion			100 billion			830 billion
698882952797896635			2183666638215038453			1551156193110436752			479479482141025770			1801480541525062987			2160424886607523104			1597842109219231701
digit	count	p	digit	count	p	digit	count	p	digit	count	p	digit	count	p	digit	count	p	digit	count	p
0	62203	0.219837	0	624485	0.501079	0	6247621	0.325702	0	62497830	0.776803	0	625007418	0.759261	0	6249955616	0.562029	0	51875094547	0.668120
1	62599	0.682549	1	625090	0.906404	1	6254262	0.078288	1	62507153	0.350065	1	625016615	0.492463	1	6249876925	0.107869	1	51874935915	0.771359
2	62367	0.582699	2	624780	0.773801	2	6248189	0.454365	2	62509711	0.204570	2	625059965	0.013239	2	6250148204	0.052852	2	51874901544	0.655269
3	62374	0.602695	3	624489	0.504410	3	6253413	0.158548	3	62492052	0.299120	3	624965876	0.158621	3	6249887252	0.140769	3	51874751046	0.258941
4	62657	0.516600	4	625478	0.532328	4	6250098	0.967706	4	62496124	0.612605	4	625035969	0.137294	4	6250071807	0.348202	4	51875054948	0.803233
5	62728	0.346239	5	625938	0.220425	5	6252653	0.273078	5	62506556	0.391737	5	624952905	0.051705	5	6249974035	0.734455	5	51874913657	0.695407
6	62686	0.442250	6	623871	0.140234	6	6249300	0.772442	6	62490736	0.226185	6	624997096	0.904507	6	6249985703	0.851837	6	51874862385	0.532612
7	62475	0.917741	7	623979	0.182260	7	6252382	0.325092	7	62490198	0.200360	7	624984572	0.523891	7	6250037947	0.620080	7	51874981860	0.934442
8	62741	0.319437	8	624160	0.272479	8	6248069	0.425026	8	62503393	0.657578	8	624971557	0.239982	8	6249954316	0.550632	8	51874976561	0.915356
9	62362	0.568608	9	624901	0.897094	9	6249176	0.733548	9	62501844	0.809633	9	625025958	0.283553	9	6250017372	0.820465	9	51874799685	0.363698
a	62600	0.679520	a	624670	0.666388	a	6248726	0.598671	a	62510012	0.190886	a	625010886	0.652912	a	6250027731	0.717146	a	51875432408	0.049905
b	62033	0.053698	b	625099	0.897094	b	6247792	0.361682	b	62499105	0.906922	b	625034903	0.149329	b	6250025978	0.734327	b	51875330194	0.134319
c	62563	0.794660	c	626077	0.159431	c	6250964	0.690449	c	62506027	0.431069	c	624986051	0.564440	c	6250100175	0.190643	c	51875197763	0.369842
d	62727	0.348358	d	625382	0.617749	d	6250397	0.869725	d	62488745	0.141468	d	624957284	0.077618	d	6249743360	0.000800	d	51874931229	0.755157
e	62686	0.442250	e	625852	0.265688	e	6254929	0.041724	e	62505903	0.440609	e	624997797	0.927485	e	6250057536	0.452263	e	51874958794	0.851777
f	62199	0.213689	f	625749	0.327832	f	6242029	0.000991	f	62494611	0.481423	f	624995148	0.841133	f	6250136043	0.075526	f	51874877464	0.578452

Euler-Mascheroni (decimal)

1 million			10 million			100 million			1 billion			10 billion			100 billion			1 trillion
382612267620472349			1619802019730642374			42278180756472665			433360971877126346			642766904453116624			1863935914261680716			1331040994867555078
digit	count	p	digit	count	p	digit	count	p	digit	count	p	digit	count	p	digit	count	p	digit	count	p
0	100150	0.617075	0	999853	0.876859	0	10001768	0.555638	0	99998397	0.865819	0	999972202	0.354134	0	10000074086	0.434841	0	100000239760	0.424174
1	100143	0.633600	1	1000601	0.526401	1	9996653	0.264565	1	100002318	0.806969	1	999920202	0.007816	1	10000028158	0.766611	1	99999957393	0.887062
2	99796	0.496504	2	998927	0.258038	2	9998112	0.529131	2	99986624	0.158553	2	999971400	0.340421	2	10000003468	0.970839	2	100000158439	0.597409
3	100194	0.517848	3	1000766	0.419416	3	9999460	0.857153	3	99984204	0.095904	3	1000007065	0.813821	3	10000079428	0.402455	3	100000186942	0.533193
4	99783	0.469475	4	1001444	0.127982	4	10007542	0.011937	4	100011681	0.218216	4	999985145	0.620482	4	9999915477	0.372956	4	100000081895	0.784866
5	100110	0.713868	5	1002104	0.026568	5	10001985	0.508185	5	99996372	0.702146	5	1000031164	0.298898	5	10000085572	0.367053	5	100000248483	0.407514
6	100170	0.570941	6	999530	0.620301	6	9996871	0.296948	6	100014127	0.136457	6	1000015349	0.608908	6	10000104446	0.270915	6	99999788061	0.479900
7	99682	0.289145	7	998692	0.167971	7	9997487	0.402218	7	99988819	0.238565	7	1000015032	0.616324	7	9999920565	0.402414	7	99999980210	0.947404
8	100135	0.652710	8	998534	0.122274	8	9998182	0.544515	8	100006202	0.513274	8	1000066616	0.026383	8	9999928916	0.453682	8	99999729332	0.366936
9	99837	0.586900	9	999549	0.634505	9	10001940	0.517848	9	100011256	0.235430	9	1000015825	0.597846	9	9999859884	0.139688	9	99999629485	0.216812

Euler-Mascheroni (hexadecimal)

1 million			10 million			100 million			1 billion			10 billion			100 billion			830 billion
289261892334479731			1965841953933984845			1148607017681645907			481768120795552997			467147817868996984			386787603304065099			737008687574482553
digit	count	p	digit	count	p	digit	count	p	digit	count	p	digit	count	p	digit	count	p	digit	count	p
0	62316	0.447172	0	624504	0.517003	0	6247664	0.334523	0	62508363	0.274597	0	625012751	0.598355	0	6249995756	0.955785	0	51875237744	0.281005
1	62562	0.797848	1	624635	0.633480	1	6247956	0.398438	1	62514792	0.053308	1	625000859	0.971692	1	6249848994	0.048526	1	51875022578	0.918454
2	62758	0.286494	2	625482	0.528903	2	6249355	0.789884	2	62512078	0.114597	2	625018299	0.449670	2	6250134660	0.078545	2	51875146311	0.507038
3	62616	0.631784	3	625012	0.987492	3	6250922	0.703281	3	62492632	0.335773	3	624988386	0.631373	3	6250017693	0.817206	3	51875156251	0.478616
4	62471	0.904638	4	625944	0.217488	4	6254030	0.095939	4	62499064	0.902678	4	625037362	0.122711	4	6249914915	0.266333	4	51874889410	0.616035
5	62789	0.232513	5	624342	0.390005	5	6246249	0.121236	5	62494447	0.468182	5	625037248	0.123857	5	6250023305	0.760781	5	51874937268	0.776056
6	62722	0.359078	6	625359	0.639073	6	6250402	0.868099	6	62504356	0.569312	6	624994180	0.809993	6	6250033092	0.665515	6	51874950064	0.820861
7	62384	0.631784	7	624203	0.297784	7	6248931	0.658762	7	62512213	0.110601	7	625024023	0.320986	7	6250016048	0.833941	7	51874834480	0.452917
8	62846	0.152892	8	626380	0.071416	8	6250486	0.840874	8	62488836	0.144714	8	624986827	0.586303	8	6249897613	0.181034	8	51875269817	0.221140
9	62185	0.193148	9	623815	0.121604	9	6250120	0.960462	9	62492925	0.355344	9	624998976	0.966257	9	6250083330	0.276322	9	51875064018	0.771592
a	62707	0.392465	a	626602	0.036363	a	6251975	0.414552	a	62493229	0.376394	a	624989151	0.654015	a	6250069862	0.361414	a	51874945954	0.806398
b	62156	0.155280	b	625182	0.812064	b	6251545	0.523299	b	62502822	0.712378	b	624999216	0.974162	b	6249989696	0.892920	b	51875101396	0.645670
c	62370	0.591231	c	624789	0.782817	c	6250143	0.952892	c	62494740	0.491980	c	624957097	0.076328	c	6249971557	0.710207	c	51875068008	0.757788
d	62213	0.235761	d	624473	0.491157	d	6250041	0.986486	d	62496663	0.662877	d	625028074	0.246135	d	6250073344	0.337981	d	51874758546	0.273566
e	62377	0.611358	e	624493	0.507752	e	6249100	0.710037	e	62492671	0.338337	e	624971034	0.231448	e	6249992750	0.924542	e	51874658093	0.121046
f	62528	0.907912	f	624785	0.778806	f	6251081	0.655178	f	62500169	0.982386	f	624956517	0.072437	f	6249937385	0.413358	f	51874960062	0.856288

Sqrt(2) (decimal)

1 million			10 million			100 million			1 billion			10 billion			100 billion			1 trillion
1046692711165650156			1029753568789489214			2243355912340480995			1427307414684103263			263041663188498021			1781018456207204053			199837451467388770
digit	count	p	digit	count	p	digit	count	p	digit	count	p	digit	count	p	digit	count	p	digit	count	p
0	99814	0.535258	0	999897	0.913542	0	10002237	0.455869	0	100010228	0.280978	0	999996989	0.920053	0	9999946091	0.569865	0	99999581178	0.162692
1	98924	0.000335	1	1000114	0.904351	1	10000179	0.952421	1	99998381	0.864493	1	1000042849	0.153206	1	10000062987	0.506728	1	99999990854	0.975679
2	100436	0.146131	2	1000208	0.826454	2	9998091	0.524559	2	99995645	0.646193	2	999987069	0.666444	2	9999903614	0.309631	2	99999633795	0.222206
3	100191	0.524342	3	999674	0.731121	3	10004178	0.163721	3	99995415	0.628882	3	999984900	0.614730	3	9999996931	0.974193	3	99999868965	0.662268
4	100024	0.936237	4	1000126	0.894339	4	10000054	0.985639	4	100012725	0.179812	4	1000008724	0.771204	4	9999963242	0.698413	4	100000203296	0.497992
5	100155	0.605389	5	999358	0.498579	5	9998344	0.580948	5	100002636	0.781121	5	999970045	0.318037	5	9999985234	0.876311	5	99999787306	0.478337
6	99886	0.703945	6	1001246	0.189048	6	10001665	0.578895	6	100012683	0.181253	6	1000007824	0.794247	6	9999930492	0.463754	6	99999740024	0.386169
7	100008	0.978726	7	999359	0.499248	7	9998646	0.651749	7	99980315	0.037988	7	999986743	0.658562	7	10000091438	0.335126	7	100000220602	0.462132
8	100441	0.141562	8	999452	0.563505	8	9996550	0.250144	8	99995120	0.606974	8	1000025363	0.397869	8	10000105868	0.264445	8	100000574888	0.055328
9	100121	0.686703	9	1000566	0.550764	9	10000056	0.985107	9	99996852	0.740019	9	999989494	0.726189	9	10000014103	0.881823	9	100000399092	0.183417

Sqrt(2) (Hexadecimal)

1 million			10 million			100 million			1 billion			10 billion			100 billion			830 billion
1693609154465577180			2008646701189710458			2172498853007019979			790271264923090951			2013374532271581726			77329400643665400			1269471280430671530
digit	count	p	digit	count	p	digit	count	p	digit	count	p	digit	count	p	digit	count	p	digit	count	p
0	62637	0.571413	0	623306	0.026895	0	6251641	0.497818	0	62500412	0.957076	0	625009536	0.693618	0	6250036529	0.633211	0	51875497886	0.023965
1	62612	0.643585	1	623806	0.118799	1	6251784	0.461121	1	62495664	0.571086	1	625016481	0.495960	1	6250066932	0.381903	1	51874726911	0.215590
2	62603	0.670464	2	626009	0.187453	2	6250155	0.948944	2	62504327	0.571885	2	625009982	0.680065	2	6249963984	0.637990	2	51874712573	0.192453
3	62109	0.106247	3	625891	0.244425	3	6252718	0.261499	3	62506782	0.375619	3	625022173	0.359663	3	6250134191	0.079591	3	51874749132	0.255297
4	62359	0.560232	4	624697	0.692225	4	6253268	0.176993	4	62494960	0.510266	4	624932165	0.005073	4	6249965672	0.653822	4	51875054346	0.805345
5	62308	0.427669	5	623847	0.131997	5	6246064	0.103943	5	62498049	0.798818	5	624986957	0.590004	5	6250085478	0.264131	5	51875122805	0.577618
6	62651	0.532753	6	626865	0.014833	6	6254526	0.061515	6	62501372	0.857751	6	625001408	0.953616	6	6249949273	0.507526	6	51874863838	0.536948
7	62500	1.000000	7	623822	0.123821	7	6248506	0.537104	7	62504606	0.547357	7	625037867	0.117734	7	6250107432	0.160472	7	51874911785	0.689144
8	63001	0.038478	8	625691	0.366675	8	6250548	0.820899	8	62505699	0.456565	8	624986428	0.575013	8	6249786998	0.005392	8	51874894872	0.633569
9	62566	0.785116	9	625263	0.731161	9	6246214	0.117802	9	62491523	0.268108	9	625002943	0.903231	9	6250164696	0.031430	9	51875272592	0.216427
a	63038	0.026244	a	625575	0.452546	a	6252253	0.351980	a	62500057	0.994059	a	625007156	0.767515	a	6249781575	0.004324	a	51874660837	0.124059
b	62245	0.292134	b	624996	0.995831	b	6246148	0.111535	b	62491022	0.240844	b	624965733	0.156883	b	6250072247	0.345256	b	51874984133	0.942642
c	62191	0.201766	c	624870	0.865143	c	6249744	0.915774	c	62498729	0.868123	c	625020586	0.395078	c	6250021808	0.775722	c	51875387625	0.078797
d	62456	0.855762	d	624878	0.873369	d	6249073	0.701749	d	62490770	0.227894	d	624990847	0.705336	d	6249989559	0.891505	d	51875043368	0.844098
e	62356	0.551917	e	624592	0.594027	e	6246368	0.133499	e	62506246	0.414515	e	625010894	0.652674	e	6249902637	0.203393	e	51875266706	0.226511
f	62368	0.585536	f	625892	0.243896	f	6250990	0.682549	f	62509782	0.201279	f	624998844	0.961910	f	6249970989	0.704689	f	51874850591	0.498086

Sqrt(3) (Decimal)

1 million			10 million			100 million			1 billion			10 billion			100 billion			1 trillion
1747852870903277898			1386305193821138555			2167416493632735487			325195415673539566			1516208769892153315			1517735239443731826			1735085482153178696
digit	count	p	digit	count	p	digit	count	p	digit	count	p	digit	count	p	digit	count	p	digit	count	p
0	100234	0.435391	0	1000172	0.856129	0	9995281	0.115719	0	99976638	0.013794	0	1000006042	0.840386	0	9999997452	0.978573	0	99999701337	0.319472
1	99587	0.168615	1	1001548	0.102735	1	10001670	0.577755	1	99988551	0.227497	1	999978902	0.481890	1	9999779898	0.020337	1	100000108745	0.716991
2	99812	0.530878	2	1000263	0.781606	2	10001751	0.559445	2	99991487	0.369533	2	999982296	0.555101	2	9999953895	0.626975	2	100000369734	0.217782
3	99818	0.544072	3	998943	0.265204	3	10000247	0.934382	3	100004464	0.637964	3	999998469	0.959299	3	9999957103	0.651144	3	100000120683	0.687480
4	99897	0.731348	4	998647	0.153814	4	10001384	0.644559	4	100023203	0.014453	4	1000009144	0.760518	4	10000130237	0.169809	4	99999923291	0.798185
5	100260	0.386125	5	999993	0.994113	5	9995879	0.169545	5	99996674	0.725895	5	999982506	0.559804	5	10000080373	0.396880	5	100000240664	0.422430
6	100558	0.062886	6	999976	0.979817	6	9999931	0.981650	6	100020148	0.033688	6	1000025094	0.402892	6	10000159003	0.093731	6	99999982497	0.953475
7	99921	0.792294	7	1000059	0.950410	7	10002655	0.376157	7	99987934	0.203420	7	999997927	0.944910	7	9999839437	0.090554	7	99999438573	0.061286
8	100055	0.854536	8	1000650	0.493243	8	10001042	0.728341	8	100017107	0.071351	8	1000013674	0.648534	8	10000016205	0.864369	8	99999785181	0.473952
9	99858	0.635975	9	999749	0.791335	9	10000160	0.957466	9	99993794	0.513002	9	1000005946	0.842889	9	10000086397	0.362451	9	100000329295	0.272357

Sqrt(3) (Hexadecimal)

1 million			10 million			100 million			1 billion			10 billion			100 billion			830 billion
25532038599112247			2188234629753134852			988190049947266222			118286717255735391			1426098788634820577			1749235982379292416			656951846402347317
digit	count	p	digit	count	p	digit	count	p	digit	count	p	digit	count	p	digit	count	p	digit	count	p
0	62715	0.374431	0	625112	0.883672	0	6253607	0.136193	0	62505175	0.499003	0	625047130	0.051532	0	6250033479	0.661845	0	51875343752	0.119052
1	62369	0.588380	1	623862	0.137100	1	6250551	0.819935	1	62493122	0.368899	1	624969213	0.203420	1	6250000940	0.990202	1	51875094659	0.667751
2	62484	0.947299	2	625330	0.666388	2	6249291	0.769598	2	62496839	0.679642	2	624985916	0.560677	2	6249867845	0.084264	2	51874740545	0.239389
3	62425	0.756684	3	626325	0.083457	3	6251149	0.635020	3	62503123	0.683283	3	625005848	0.809097	3	6249969723	0.692447	3	51874794767	0.352039
4	62386	0.637673	4	625469	0.540075	4	6249679	0.894501	4	62512112	0.113580	4	625037355	0.122781	4	6250043003	0.574260	4	51874996176	0.986165
5	62929	0.076349	5	626200	0.116957	5	6254735	0.050452	5	62514821	0.052842	5	625007601	0.753513	5	6249945512	0.476571	5	51874708594	0.186369
6	62629	0.594087	6	624441	0.465222	6	6254624	0.056100	6	62498708	0.865965	6	625000101	0.996671	6	6250009702	0.899141	6	51874782656	0.324349
7	62305	0.420485	7	624733	0.727234	7	6244159	0.015821	7	62488329	0.127336	7	624976594	0.333572	7	6250000045	0.999531	7	51874654905	0.117617
8	62687	0.439800	8	625227	0.766809	8	6252291	0.343917	8	62497096	0.704408	8	625011135	0.645511	8	6250020602	0.787819	8	51875000672	0.997569
9	62564	0.791475	9	623968	0.177594	9	6247221	0.250946	9	62494177	0.446828	9	625024585	0.309796	9	6250091419	0.232363	9	51875184637	0.402453
a	62214	0.237397	a	624509	0.521237	a	6249674	0.892868	a	62498742	0.869460	a	624979817	0.404396	a	6249913360	0.257693	a	51875060511	0.783784
b	62247	0.295936	b	625972	0.204150	b	6248074	0.426226	b	62496357	0.634132	b	625007671	0.751317	b	6250071822	0.348101	b	51875320334	0.146342
c	62909	0.091094	c	625641	0.402368	c	6248566	0.553575	c	62498378	0.832187	c	624994444	0.818458	c	6249977905	0.772851	c	51875212484	0.335286
d	62701	0.406331	d	625094	0.902265	d	6246836	0.191177	d	62499506	0.948544	d	624978296	0.369915	d	6250053256	0.486596	d	51874818125	0.409529
e	61870	0.009251	e	623884	0.144858	e	6251073	0.657566	e	62504003	0.601009	e	625004931	0.838581	e	6249960521	0.606028	e	51874983855	0.941639
f	62566	0.785116	f	624233	0.316341	f	6248470	0.527341	f	62499512	0.949168	f	624969363	0.205631	f	6250040866	0.593431	f	51875303328	0.168989

Log(5) (decimal)

1 million			10 million			100 million			1 billion			10 billion			100 billion			1 trillion
703044299066299434			918808029013683101			48233278362098083			676338011530928150			679402724571734092			183026502790557771			1674275876876480658
digit	count	p	digit	count	p	digit	count	p	digit	count	p	digit	count	p	digit	count	p	digit	count	p
0	99739	0.384300	0	999843	0.868556	0	10004262	0.155414	0	100005963	0.529640	0	999967520	0.278956	0	9999910417	0.345023	0	100000144668	0.629645
1	100402	0.180245	1	999873	0.893506	1	9998100	0.526516	1	99991685	0.380770	1	1000041188	0.169773	1	10000000053	0.999554	1	100000213975	0.475691
2	99692	0.304577	2	1001026	0.279475	2	9997874	0.478531	2	100005713	0.547039	2	1000010225	0.733229	2	9999867064	0.161134	2	99999970729	0.922274
3	100151	0.614730	3	1000170	0.857784	3	9999085	0.760366	3	99980522	0.040057	3	999944151	0.062655	3	9999895051	0.268614	3	99999887031	0.706498
4	99866	0.655116	4	1000523	0.581435	4	10002698	0.368475	4	100017933	0.058717	4	1000026944	0.369114	4	10000015772	0.867959	4	99999408118	0.048502
5	99292	0.018275	5	998958	0.272045	5	9996704	0.271913	5	100006274	0.508396	5	999992885	0.812527	5	10000036251	0.702373	5	100000268280	0.371179
6	100271	0.366349	6	999186	0.390875	6	10003378	0.260166	6	100010082	0.287902	6	1000057524	0.055179	6	10000146211	0.123268	6	100000579496	0.053402
7	100337	0.261296	7	1000292	0.758238	7	9994626	0.073240	7	99989512	0.268929	7	999964927	0.242363	7	10000127255	0.179795	7	99999496923	0.093557
8	100365	0.223731	8	1001519	0.109340	8	10003623	0.227176	8	100004944	0.602267	8	999993351	0.824599	8	9999897884	0.281750	8	99999800985	0.507085
9	99885	0.701473	9	998610	0.142869	9	9999650	0.907124	9	99987372	0.183153	9	1000001285	0.965834	9	10000104042	0.272773	9	100000229795	0.443686

Log(5) (Hexadecimal)

1 million			10 million			100 million			1 billion			10 billion			100 billion			830 billion
1748273793987110168			190106528688793635			1781213602437251070			12003363694091976			2164028288578754088			774100575143007341			2218095198310134979
digit	count	p	digit	count	p	digit	count	p	digit	count	p	digit	count	p	digit	count	p	digit	count	p
0	62251	0.303637	0	624011	0.196349	0	6251833	0.448903	0	62504450	0.561008	0	625003361	0.889569	0	6249966934	0.665761	0	51874830253	0.441461
1	62335	0.495463	1	626033	0.177175	1	6252993	0.216287	1	62502160	0.777805	1	625065239	0.007036	1	6250102609	0.180090	1	51875110419	0.616581
2	62250	0.301700	2	624419	0.447843	2	6246847	0.192724	2	62501294	0.865759	2	624992204	0.747402	2	6250020021	0.793666	2	51875149574	0.497612
3	62611	0.646549	3	625200	0.793877	3	6246726	0.176200	3	62499310	0.928175	3	625000849	0.972021	3	6249973238	0.726626	3	51874581940	0.057997
4	62508	0.973635	4	625036	0.962489	4	6251399	0.563296	4	62492888	0.352833	4	625000440	0.985497	4	6249958935	0.591633	4	51874592747	0.064789
5	62838	0.162612	5	626063	0.164925	5	6249356	0.790202	5	62499102	0.906611	5	624989182	0.654939	5	6249965152	0.648928	5	51875060863	0.782558
6	62528	0.907912	6	624994	0.993746	6	6251800	0.457111	6	62500761	0.920807	6	624968062	0.187030	6	6250026095	0.733176	6	51874932050	0.757988
7	62436	0.791475	7	623664	0.080925	7	6247066	0.225478	7	62503737	0.625408	7	625012408	0.608233	7	6250080936	0.290355	7	51875015521	0.943890
8	62794	0.224531	8	624662	0.658807	8	6247687	0.339303	8	62500826	0.914069	8	625003388	0.888688	8	6249914896	0.266227	8	51874686250	0.154818
9	61969	0.028260	9	624559	0.564534	9	6249512	0.840228	9	62500703	0.926826	9	625042543	0.078828	9	6250017263	0.821573	9	51874919273	0.714319
a	62485	0.950589	a	624836	0.830353	a	6251048	0.665053	a	62497162	0.710820	a	624986181	0.568076	a	6250102955	0.178626	a	51875376211	0.088017
b	62286	0.376657	b	625874	0.253542	b	6254420	0.067853	b	62504780	0.532328	b	625007302	0.762912	b	6250004783	0.950177	b	51874878446	0.581501
c	62977	0.048773	c	625443	0.562769	c	6252385	0.324483	c	62493556	0.399877	c	624974753	0.296948	c	6249852557	0.054081	c	51875373010	0.090753
d	62661	0.505974	d	624956	0.954162	d	6247774	0.357781	d	62490743	0.226536	d	624949177	0.035765	d	6249958378	0.586615	d	51874937963	0.778472
e	62325	0.469706	e	625031	0.967696	e	6249168	0.731061	e	62506049	0.429389	e	624991881	0.737315	e	6249994240	0.940017	e	51875281394	0.201956
f	62746	0.309500	f	625219	0.774801	f	6249986	0.995385	f	62502479	0.746048	f	625013030	0.590375	f	6250061008	0.425448	f	51875274086	0.213919

Log(7) (Decimal)

1 million			10 million			100 million			1 billion			10 billion			100 billion			1 trillion
2170127050664559719			1552391703744652999			1679802679062447284			1076125828365528209			1863341590108441759			1772211777571783439			341488802486929017
digit	count	p	digit	count	p	digit	count	p	digit	count	p	digit	count	p	digit	count	p	digit	count	p
0	100045	0.880765	0	1000025	0.978976	0	10000655	0.827169	0	100006155	0.516472	0	999990362	0.748008	0	9999831730	0.076109	0	100000043031	0.885945
1	100174	0.561915	1	998742	0.184824	1	9996434	0.234571	1	100005287	0.577323	1	999994826	0.863071	1	10000082586	0.384009	1	99999874909	0.676700
2	99495	0.092311	2	1000334	0.724788	2	10000060	0.984043	2	99991375	0.363268	2	999940449	0.047141	2	9999880242	0.206819	2	99999878355	0.685122
3	100407	0.174887	3	1000890	0.348171	3	10002212	0.460920	3	99991226	0.355038	3	999943314	0.058820	3	10000051796	0.585081	3	100000356381	0.234858
4	100097	0.746443	4	1000149	0.875198	4	10007129	0.017486	4	100016771	0.077091	4	1000028183	0.347508	4	10000033360	0.725104	4	100000066102	0.825606
5	99355	0.031555	5	999101	0.343318	5	9997045	0.324624	5	100016468	0.082585	5	1000009522	0.750940	5	9999927583	0.445259	5	99999969176	0.918164
6	99961	0.896566	6	1001547	0.102958	6	9995796	0.161114	6	99980487	0.039701	6	1000010723	0.720767	6	10000018603	0.844538	6	99999923821	0.799550
7	99884	0.699003	7	1000268	0.777563	7	9996589	0.255538	7	99999725	0.976875	7	1000034593	0.248869	7	9999990841	0.923088	7	99999669962	0.271277
8	100391	0.192461	8	998617	0.144893	8	10003682	0.219697	8	99994554	0.565928	8	1000013745	0.646833	8	10000076919	0.417482	8	100000183743	0.540222
9	100191	0.524342	9	1000327	0.730329	9	10000398	0.894457	9	99997952	0.829083	9	1000034283	0.253135	9	10000106340	0.262321	9	100000034520	0.908392

Log(7) (Hexadecimal)

1 million			10 million			100 million			1 billion			10 billion			100 billion			830 billion
369763193287678116			1512171041039419856			2279554978310891745			275778849044846410			88515534409896199			1413362727155526216			1868623220042046057
digit	count	p	digit	count	p	digit	count	p	digit	count	p	digit	count	p	digit	count	p	digit	count	p
0	62357	0.554682	0	625166	0.828316	0	6253173	0.189917	0	62507056	0.356637	0	625026440	0.274708	0	6250010239	0.893591	0	51875291148	0.186759
1	62080	0.082724	1	626038	0.175087	1	6250981	0.685280	1	62504925	0.519965	1	625022522	0.352151	1	6250082769	0.279568	1	51874748921	0.254898
2	62536	0.881773	2	625897	0.241263	2	6250003	0.999011	2	62488605	0.136583	2	624999508	0.983784	2	6249914363	0.263244	2	51875112096	0.611239
3	62191	0.201766	3	624583	0.585914	3	6251338	0.580433	3	62496057	0.606475	3	625011711	0.628526	3	6249961175	0.612009	3	51874958343	0.850174
4	62074	0.078428	4	624563	0.568071	4	6247937	0.394068	4	62493856	0.422178	4	625006532	0.787277	4	6250124248	0.104553	4	51875075552	0.731903
5	62483	0.944011	5	624002	0.192308	5	6250567	0.814800	5	62496578	0.654840	5	625040218	0.096617	5	6250053200	0.487054	5	51875294872	0.181185
6	62613	0.640626	6	624594	0.595837	6	6247923	0.390867	6	62505931	0.438444	6	624989953	0.678098	6	6250008700	0.909510	6	51875099417	0.652125
7	62449	0.833129	7	624666	0.662593	7	6249794	0.932180	7	62478878	0.005791	7	624978208	0.367978	7	6250096131	0.209170	7	51874970916	0.895077
8	62772	0.261148	8	625113	0.882641	8	6251472	0.543115	8	62507000	0.360467	8	625044626	0.065244	8	6250083701	0.274190	8	51875116680	0.596741
9	62733	0.335766	9	625188	0.805990	9	6248731	0.600107	9	62500454	0.952705	9	624998546	0.952102	9	6250005584	0.941847	9	51874930028	0.751022
a	62610	0.649519	a	625648	0.397250	a	6246883	0.197854	a	62497978	0.791662	a	624944252	0.021276	a	6249880850	0.119573	a	51875122226	0.579414
b	62718	0.367802	b	624200	0.295970	b	6250900	0.710037	b	62521106	0.005829	b	625015500	0.521956	b	6249967584	0.671944	b	51874870522	0.557119
c	62952	0.061860	c	625157	0.837491	c	6250025	0.991760	c	62504923	0.520135	c	624959476	0.094107	c	6249929333	0.355908	c	51874996696	0.988046
d	62153	0.151709	d	624597	0.598557	d	6251588	0.511804	d	62502151	0.778706	d	625003026	0.900516	d	6249911453	0.247365	d	51874938390	0.779958
e	62797	0.219837	e	625875	0.252999	e	6250712	0.768651	e	62499841	0.983428	e	624977365	0.349740	e	6249943112	0.457372	e	51874661517	0.124815
f	62482	0.940723	f	624713	0.707709	f	6247973	0.402373	f	62494661	0.485500	f	624982117	0.460041	f	6250027558	0.718835	f	51874812676	0.395641