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Primes of form n^6-(n+1)^5.
2

%I #8 Mar 06 2019 13:40:51

%S 971,431441,838949,2614691,6770161,43845881,570523321,9244951889,

%T 33640090481,41402933641,81303824909,126165366289,137240997911,

%U 346860978491,372445245449,525200678549,726938163649,774170449439

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

%C (1) It is conjectured that sequence is infinite.

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

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

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

%H Harvey P. Dale, <a href="/A171771/b171771.txt">Table of n, a(n) for n = 1..1000</a>

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

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

%Y Cf. A002327, A140719, A087191

%K nonn

%O 1,1

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

%E Edited by _D. S. McNeil_, Nov 21 2010