A050920 Cullen primes: primes of the form n*2^n+1.

3, 393050634124102232869567034555427371542904833

Offset: 1

Author

N. J. A. Sloane, Dec 30 1999

Keywords

• nonn
• nice
• bref

Comments

The next term is too large to display here, having 1423 digits. See A005849.

Examples

			1 * 2^1 + 1 = 3, which is prime.
141 * 2^141 + 1 = 393050634124102232869567034555427371542904833, which is also prime.
The third Cullen prime is approximately 2.677114856136697933736444 * 10^1422.
		

References

• R. K. Guy, Unsolved Problems in Number Theory, Springer, 1st edition, 1981. See section B20.

Links

• Ray Ballinger, Cullen Primes: Definition and Status.
• Chris K. Caldwell, Cullen Primes.
• Eric Weisstein's World of Mathematics, Cullen Number.

Crossrefs

See A005849 for the corresponding n.

Cf. A002064.

Programs

Mathematica

Select[Table[n * 2^n + 1, {n, 5000}], PrimeQ] (* Harvey P. Dale, Dec 14 2014 *)

Formula

a(n) = A002064(A005849(n)).