A132216 Primes that are sums of eighth powers of two distinct primes.

815730977, 124097929967680577, 6115597639891380737, 144086718355753024097, 524320466699664691937, 3377940044732998170977, 10094089678769799935777, 30706777728209453204417, 58310148000746221725857

Offset: 1

Author

Jonathan Vos Post, Aug 13 2007

Keywords

• easy
• nonn

Comments

These primes exist because the polynomial x^8 + y^8 is irreducible over Z. Note that 2^8 + n^8 can be prime for composite n beginning 21, 55, 69, 77, 87, 117.

Examples

			a(1) = 2^8 + 13^8 = 256 + 815730721 = 815730977, which is prime.
a(2) = 2^8 + 137^8 = 124097929967680577, which is prime.
a(3) = 2^8 + 223^8 = 6115597639891380737, which is prime.
a(4) = 2^8 + 331^8 = 144086718355753024097, which is prime.
a(5) = 2^8 + 389^8 = 524320466699664691937, which is prime.
a(6) = 2^8 + 491^8 = 3377940044732998170977, which is prime.
a(7) = 2^8 + 563^8 = 10094089678769799935777, which is prime.
		

Crossrefs

Cf. A000040, A001016, A050997, A120398, A122616, A130873, A130555, A132214, A132215.

Formula

Primes in A132215. {A001016(A000040(i)) + A001016(A000040(j)) for i > j and are elements of A000040}.

Extensions

More terms from Jon E. Schoenfield, Jul 16 2010