A059609 Numbers k such that 2^k - 7 is prime.

39, 715, 1983, 2319, 2499, 3775, 12819, 63583, 121555, 121839, 468523, 908739

Offset: 1

Author

Andrey V. Kulsha, Feb 02 2001

Keywords

• nonn
• more

Examples

			k = 39, 2^39 - 7 = 549755813881 is prime.
		

References

• J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 39, p. 15, Ellipses, Paris 2008.
• J.-M. De Koninck and A. Mercier, 1001 Problemes en Theorie Classique Des Nombres, Problem 395 pp. 55; 218, Ellipses Paris 2004.
• Wacław Sierpiński, Co wiemy, a czego nie wiemy o liczbach pierwszych. Warsaw: PZWS, 1961, pp. 46-47.
• Wacław Sierpiński, O stu prostych, ale trudnych zagadnieniach arytmetyki. Warsaw: PZWS, 1959, pp. 31, 75.

Links

• Keith Conrad, Square patterns and infinitude of primes, University of Connecticut, 2019.
• Jon Grantham and Andrew Granville, Fibonacci primes, primes of the form 2^n-k and beyond, arXiv:2307.07894 [math.NT], 2023.
• Henri Lifchitz and Renaud Lifchitz, Search for 2^n-7, PRP Top Records.

Crossrefs

Cf. A096502.

Cf. Sequences of numbers k such that 2^k - d is prime: A000043 (d=1), A050414 (d=3), A059608 (d=5), this sequence (d=7), A059610 (d=9), A096817 (d=11), A096818 (d=13), A059612 (d=15), A059611 (d=17), A096819 (d=19), A096820 (d=21), A057220 (d=23), A356826 (d=29).

Programs

Mathematica

Select[Range[3, 20000], PrimeQ[2^# - 7] &] (* Vladimir Joseph Stephan Orlovsky, Feb 26 2011 *)

PARI

is(n)=isprime(2^n-7) \\ Charles R Greathouse IV, Feb 17 2017

Extensions

a(8) from Henri Lifchitz, a(9)-a(10) from Gary Barnes, added by Max Alekseyev, Feb 09 2012

a(11) from Lelio R Paula, added by Max Alekseyev, Oct 25 2015

a(12) from Jon Grantham, Aug 09 2023