A171771 Primes of form n^6-(n+1)^5.

971, 431441, 838949, 2614691, 6770161, 43845881, 570523321, 9244951889, 33640090481, 41402933641, 81303824909, 126165366289, 137240997911, 346860978491, 372445245449, 525200678549, 726938163649, 774170449439

Offset

1,1

Comments

(1) It is conjectured that sequence is infinite.

(2) p=97=prime(25) is the smallest prime such that (p-1)^6-p^5 and p^6-(p+1)^5 are primes.

References

Leonard E. Dickson: History of the Theory of numbers, vol. I, Dover Publications 2005

Derrick H. Lehmer, Guide to Tables in the Theory of Numbers Washington, D.C. 1941

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Example

4^6-5^5=971 and 9^6-10^5=431441 are prime.

Mathematica

Select[Table[n^6-(n+1)^5, {n, 3, 100}], PrimeQ] (* Harvey P. Dale, Mar 06 2019 *)

Crossrefs

Cf. A002327, A140719, A087191

Sequence in context: A257975 A217161 A243861 * A206089 A217162 A203375

Adjacent sequences: A171768 A171769 A171770 * A171772 A171773 A171774

Keyword

nonn

Author

Ulrich Krug (leuchtfeuer37(AT)gmx.de), Dec 18 2009

Extensions

Edited by D. S. McNeil, Nov 21 2010

Status

approved