|
Search: id:A132216
|
|
|
| A132216 |
|
Primes that are sums of eighth powers of two distinct primes. |
|
+0
5
|
|
| 815730977, 124097929967680577, 6115597639891380737, 144086718355753024097, 524320466699664691937, 3377940044732998170977, 10094089678769799935777
(list; graph; listen)
|
|
|
OFFSET
|
1,1
|
|
|
COMMENT
|
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.
|
|
FORMULA
|
Primes in A132215. {A001016(A000040(i)) + A001016(A000040(j)) for i > j and are elements of A000040}.
|
|
EXAMPLE
|
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.
Sequence in context: A166072 A152156 A017540 this_sequence A091340 A114665 A157798
Adjacent sequences: A132213 A132214 A132215 this_sequence A132217 A132218 A132219
|
|
KEYWORD
|
easy,more,nonn
|
|
AUTHOR
|
Jonathan Vos Post (jvospost3(AT)gmail.com), Aug 13 2007
|
|
|
Search completed in 0.002 seconds
|
