A094475 Primes of form 2^n + 5^n.

2, 7, 29, 641

Offset

1,1

Comments

2^n+p^n is prime if n=0;or n=1 and p is a smaller of twin primes; or n=2 and 4+p^2 is prime; or n=3 and 8+p^3 is prime etc. Several conditions have to be satisfied to get a modest number of terms...

n must be zero or a power of two. Checked n being powers of two through 2^22. Thus a(5) > 10^5800000. Primes of this magnitude are rare (about 1 in 13.4 million), so chance of finding one is remote with today's computer algorithms and speeds. - Robert Price, May 02 2013

Links

Table of n, a(n) for n=1..4.

Example

For n=4, p=2^4+5^4=641, so p can be prime even when the exponent is not a prime.

Mathematica

Select[Table[2^n+5^n, {n, 0, 5000}], PrimeQ] (* Harvey P. Dale, May 28 2014 *)

Prog

(Magma) [ a: n in [0..2100] | IsPrime(a) where a is 5^n+2^n]; // Vincenzo Librandi, Nov 18 2010

Crossrefs

Cf. A094473, A094474, A082101, A094476.

Sequence in context: A192410 A270518 A359950 * A093034 A125174 A270526

Adjacent sequences: A094472 A094473 A094474 * A094476 A094477 A094478

Keyword

nonn,easy

Author

Labos Elemer, Jun 01 2004

Status

approved