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A082101
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Primes of form 2^k + 3^k.
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38
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OFFSET
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1,1
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COMMENTS
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Since x+y is a factor of x^m+y^m if m is odd, 2^m+3^m is divisible by 2+3=5 unless m is zero or a power of 2. This is similar to Fermat numbers 1+2^m. - Michael Somos, Aug 27 2004
Checked k being powers of two through 2^21. Thus a(5) > 10^2000000. Primes of this magnitude are rare (about 1 in 4.6 million), so chance of finding one is remote with today's computer algorithms and speeds. - Robert Price, Apr 25 2013
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LINKS
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EXAMPLE
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m=0: 1+1, m=1: 2+3, m=2: 4+9, m=4: 16+81.
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MATHEMATICA
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Select[Table[2^k+3^k, {k, 0, 100}], PrimeQ] (* Harvey P. Dale, May 14 2014 *)
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PROG
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(PARI) print1(2); for(n=0, 99, if(ispseudoprime(t=2^(2^n)+3^(2^n)), print1(", "t))) \\ Charles R Greathouse IV, Jul 19 2011
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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