A104851 Primes from merging of 10 successive digits in decimal expansion of e.

7427466391, 7413596629, 6059563073, 3490763233, 2988075319, 1573834187, 7021540891, 5408914993, 6480016847, 9920695517, 1838606261, 6062613313, 3845830007, 1692836819, 4425056953, 2505695369, 5490598793, 1782154249, 8215424999, 9229576351, 9519366803

Offset: 1

Author

Andrew G. West (WestA(AT)wlu.edu), Mar 27 2005

Keywords

• nonn
• base

Comments

Scan decimal expansion of e from left to right, recording any 10-digit primes seen. - N. J. A. Sloane, Feb 05 2012

All the primes listed here must have 10 digits, i.e., "leading zeros are not allowed". Otherwise, one would also have some terms as 297606737 or 865746377 or 98793127 from A104850. - M. F. Hasler, Nov 01 2014

The original version read (1185790117, 1180978417, 1573834187, 1838606261, 1308008771, 1692836819, 1782154249, 1825288693, 1525971943, 1730123819, 1332069811, 1881593041, 1934580727, 1978623209, 1164218399, 1574862173, 1635834619, 1311914371, ...). These terms are obtained when using signed 32-bit integers, i.e., take the 10-digit numbers modulo 2^32, and select the primes between 10^9 and 2^31. - M. F. Hasler, Nov 01 2014

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Crossrefs

For e, see also A104843, A104844, A104845, A104846, A104847, A104848, A104849, A104850, A104851 (this).

For Pi, see A198175, A198170, A104824, A104825, A104826, A198171, A198172, A198173, A198174.

For sqrt(2), see A198162, A198163, A198164, A198165, A198166, A198167, A198168, A198169, A198161.

For the Golden Ratio, see A198177, A103773, A103789, A103793, A103808, A103809, A103810, A103811, A103812; A103752.

For the Euler-Mascheroni constant gamma: A198776, A198777, A198778, A198779, A198780, A198781, A198782, A198783, A198784.

Programs

Mathematica

With[{de=FromDigits/@Partition[RealDigits[E,10,10000][[1]],10,1]}, Select[de,#>10^9&&PrimeQ[#]&]] (* Harvey P. Dale, Feb 05 2012 *)

PARI

list_A104851(x=exp(1), m=10)=m=10^m; for(k=1, default(realprecision), isprime(p=x\.1^k%m)&&p*10>m&&print1(p", ")) \\ The optional arguments can be used to produce other sequences of this series (cf. Crossrefs). Use e.g. \p999 to set precision to 999 digits. - M. F. Hasler, Nov 01 2014

Extensions

Corrected by Harvey P. Dale, Feb 05 2012

Offset changed from 0 to 1 by Vincenzo Librandi, Apr 21 2013