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A132216
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Primes that are sums of eighth powers of two distinct primes.
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4
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815730977, 124097929967680577, 6115597639891380737, 144086718355753024097, 524320466699664691937, 3377940044732998170977, 10094089678769799935777, 30706777728209453204417, 58310148000746221725857
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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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.
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FORMULA
| Primes in A132215. {A001016(A000040(i)) + A001016(A000040(j)) for i > j and are elements of A000040}.
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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.
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CROSSREFS
| Cf. A000040, A001016, A050997, A120398, A122616, A130873, A130555, A132214, A132215.
Sequence in context: A166072 A152156 A017540 * A091340 A114665 A204406
Adjacent sequences: A132213 A132214 A132215 * A132217 A132218 A132219
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KEYWORD
| easy,nonn
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AUTHOR
| Jonathan Vos Post (jvospost3(AT)gmail.com), Aug 13 2007
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EXTENSIONS
| More terms from Jon E. Schoenfield (jonscho(AT)hiwaay.net), Jul 16 2010
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