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

Author

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

Keywords

• nonn

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.

Examples

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

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

Crossrefs

Cf. A002327, A140719, A087191

Programs

Mathematica

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

Extensions

Edited by D. S. McNeil, Nov 21 2010