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Search: id:A123250
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| A123250 |
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Primes of the form 2^n + 5. |
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+0
2
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| 7, 13, 37, 2053, 140737488355333, 9007199254740997, 2787593149816327892691964784081045188247557, 11150372599265311570767859136324180752990213
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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If 2^n + 5 is prime then n is odd. Proof: Lemma 1: a^n+b^n = (a+b)(a^n-1 - a^(n-2)b + ... + b^(n-1)) 2^n + 5 = 2*(2^(n-1)+1) + 3. Then if n is even, n-1 is odd and by Lemma 1, 2+1 divides 2*(2^(n-1)+1) and thus divides 2^n+5 so it cannot be prime.
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PROGRAM
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(PARI) g(n, p) = for(k=1, n, y=p+2^k; if(isprime(y), print1(y", ")))
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CROSSREFS
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Sequence in context: A094069 A052378 A090607 this_sequence A062591 A056249 A107207
Adjacent sequences: A123247 A123248 A123249 this_sequence A123251 A123252 A123253
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KEYWORD
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nonn
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AUTHOR
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Cino Hilliard (hillcino368(AT)gmail.com), Oct 08 2006
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