A228033 Primes of the form 8^k + 5.

13, 2787593149816327892691964784081045188247557, 15177100720513508366558296147058741458143803430094840009779784451085189728165691397

Offset: 1

Author

Vincenzo Librandi, Aug 11 2013

Keywords

• nonn
• hard
• bref

Comments

a(4) = 8^64655 + 5 = 1.919...*10^58389 is too large to include. - Amiram Eldar, Jul 23 2025

Crossrefs

Cf. A217355 (associated n).

Cf. Primes of the form k^n + h: A092506 (k=2, h=1), A057733 (k=2, h=3), A123250 (k=2, h=5), A104066 (k=2, h=7), A104070 (k=2, h=9), A057735 (k=3, h=2), A102903 (k=3, h=4), A102870 (k=3, h=8), A102907 (k=3, h=10), A290200 (k=4, h=1), A182330 (k=5, h=2), A102910 (k=5, h=8), A182331 (k=6, h=1), A104118 (k=6, h=5), A104115 (k=6, h=7), A104065 (k=7, h=4), this sequence (k=8, h=5), A144360 (k=8, h=7), A145440 (k=8, h=9), A228034 (k=9, h=2), A159352 (k=10, h=3), A159031 (k=10, h=7).

Programs

Magma

[a: n in [1..300] | IsPrime(a) where a is 8^n+5];

Mathematica

Select[Table[8^n + 5, {n, 4000}], PrimeQ]