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A157950 Primes p such that p^8 + 2^8 is prime. 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
17 divides p^8 + 2^8 if k is odd and p = 17k +- 6, 17k +- 10, 17k +- 12, 17k +- 14, so only 8 integers p in each interval of length 34 need to be tested for the primality of p and of p^8 + 2^8: those of the forms p = 17k +- 2 (which yield terms 223, 389, 491, 563, 797, 1579, 3313, 3623, 3691, ...), p = 17k +- 4 (which yield terms 13, 701, 2027, 2087, 2333, 2393, 2699, ...), p = 17k +-8 (which yield terms 331, 773, 1063, 1181, 1811, 2269, ...), and p = 17k +-16 (which yield terms 137, 647, 1531, 2617, 2687, 2857, 3467, 3637, ...).
It is conjectured that this sequence is infinite.
REFERENCES
Leonard E. Dickson, History of the Theory of Numbers.
Richard Guy, Unsolved Problems in Number Theory.
LINKS
EXAMPLE
n=11: 11^8 + 2^8 = 214359137 = 17 * 241 * 52321, not prime, so 11 is not a term;
n=13: 13^8 + 2^8 = 815730977 is prime, so 13 is a term.
MAPLE
a := proc (n) if isprime(ithprime(n)^8+256) = true then ithprime(n) else end if end proc: seq(a(n), n = 1 .. 900); # Emeric Deutsch, Mar 14 2009
CROSSREFS
Sequence in context: A078795 A123299 A142017 * A249444 A046278 A016205
KEYWORD
nonn
AUTHOR
Ulrich Krug (leuchtfeuer37(AT)gmx.de), Mar 10 2009
EXTENSIONS
Definition corrected by Emeric Deutsch, Mar 14 2009
Extended by Emeric Deutsch, Mar 14 2009
Edited by Jon E. Schoenfield, Jan 29 2019
STATUS
approved

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Last modified March 29 06:15 EDT 2024. Contains 371265 sequences. (Running on oeis4.)