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Search: id:A157950
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| A157950 |
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Numbers p such that both p and p^8+2^8 are prime. |
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3
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| 13, 137, 223, 331, 389, 491, 563, 647, 701, 773, 797, 1063, 1181, 1531, 1579, 1811, 2027, 2087, 2269, 2333, 2393, 2617, 2687, 2699, 2857, 3313, 3467, 3623, 3637, 3691, 3739, 3761, 3863, 3877, 4133, 4201, 4283, 4297, 4877, 5023, 5839, 5897, 6043, 6053
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OFFSET
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1,1
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COMMENT
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Notes: 1) primes n^8+2^8 only for odd n 2) divisor 17 if n=17k +/- 6, n=17k +/- 10, n=17k +/- 12, n=17k +/- 14, so calculation only for primes of the form n=17k+/-2 => 223,389,491,563,797,1579,3313,3623,3691,... n=17k+/-4 => 13,701,2027,2087,2333,2393,2699,... n=17k+/-8 => 331,773,1063,1181,1811,2269,... n=17k+/-16 => 137,647,1531,2617,2687,2857,3467,3637,... (only 8 natural numbers in each interval of length 34) 3) it is conjectured that sequence a(n) is infinite
n^8+2^8 has divisor 17 if n=17k +/- 6, n=17k +/- 10, n=17k +/- 12, n=17k +/- 14 where k = 1, 3, 5, ....
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REFERENCES
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Leonard E. Dickson, History of the Theory of Numbers
Richard Guy, Unsolved Problems in Number Theory
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FORMULA
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n^8+2^8 and n to be a prime
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EXAMPLE
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n=11: 11^8+2^8=214359137=17 x 241 x 52321 no prime n=13: 13^8+2^8=815730977 is prime => a(1)=13
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MAPLE
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a := proc (n) if isprime(ithprime(n)^8+256) = true then ithprime(n) else end if end proc: seq(a(n), n = 1 .. 900); [From Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 14 2009]
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CROSSREFS
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A062324 A157764
Sequence in context: A078795 A123299 A142017 this_sequence A046278 A016205 A083755
Adjacent sequences: A157947 A157948 A157949 this_sequence A157951 A157952 A157953
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KEYWORD
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nonn
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AUTHOR
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Ulrich Krug (leuchtfeuer37(AT)gmx.de), Mar 10 2009
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EXTENSIONS
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Definition corrected by Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 14 2009
Extended by Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 14 2009
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