A049014 -id:A049014 - cp's OEIS frontend

A108251 Numbers n such that googol - n is prime.

797, 911, 1287, 2127, 2217, 2247, 2303, 2457, 2841, 3221, 3407, 3531, 3921, 4353, 4361, 4403, 5097, 5459, 5867, 6173, 6261, 6531, 6741, 6939, 7133, 7271, 7311, 7707, 7797, 8651, 8841, 8951, 9347, 9401, 9599, 9669, 9729, 10001, 10773, 10937, 11663

Offset: 1

Cino Hilliard, Jun 17 2005

This sequence is finite with between 4.361969*10^97 and 4.361998*10^97 terms. Under the Riemann Hypothesis, it has 4.361971987140703159099509113229164611538757211...*10^97 terms. - Charles R Greathouse IV, Nov 23 2009

10^100-a(148) and 10^100-a(149) are the last twin primes less than 10^100. - T. D. Noe, Nov 03 2008

			A googol = 10^100. 10^100 - 797 is prime, so 797 is in the sequence.

T. D. Noe, Table of n, a(n) for n = 1..1000
For each of the 1000 terms in the table, 10^100 - a(n) was verified by the Magma Calculator as prime. - _Jon E. Schoenfield_, Aug 24 2009

Cf. A049014, A133282.

Rest[10^100-#&/@NestList[NextPrime[#,-1]&,10^100,50]] (* Harvey P. Dale, Jan 23 2017 *)

forstep(x=1,n,2,if(isprime(10^100-x),print1(x",")))

Edited by Charles R Greathouse IV, Nov 23 2009

A076848 Smallest prime factor of googol + n that exceeds 13, or 1 if googol + n is 13-smooth.

Original entry on oeis.org

73, 4832936419, 157, 20794121, 127, 859493, 557, 113, 3221, 19, 7549, 43, 17, 61, 211, 241, 18617, 907, 419, 47, 443, 911, 47955653711170550856726386495271851, 1109, 53, 31, 37, 2543, 19, 17, 617, 33521, 23, 7906914473, 38851, 421, 39640576062095087

Offset: 1

Jason Earls, Nov 23 2002

nonn

A googol is 10^100. Factors found using PARI and Dario Alpern's ECM factorization applet.

Sean A. Irvine, Table of n, a(n) for n = 1..1000 (terms 1..400 from Charles R Greathouse IV, n=260 corrected by Sean A. Irvine)
Dario Alpern, Factorization using the Elliptic Curve Method

Cf. A049014 (n such that googol + n is prime), A066298, A080197 (relates to positions of 1's).
Equivalent sequences: A072288 (googolplex + n), A078813 (googol - n).
See the formula section for the relationships with A007947, A020639, A034386.

a(n) = A020639(A007947(10^100 + n)/gcd(10^100 + n, A034386(13))), where A020639(m) = lpf(m), smallest prime factor of m. - Peter Munn, Feb 20 2025

a(23) found by Sean A. Irvine on Dec 08 2002 by employing SNFS, using the polynomials x^5+23 and x-10^20.
Edited by Robert G. Wilson v, Dec 09 2002
Edited by Peter Munn, Feb 20 2025

cp's OEIS Frontend

A108251 Numbers n such that googol - n is prime.

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