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A078902
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Generalized Fermat primes of the form (k+1)^2^m + k^2^m, with m>1.
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9
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17, 97, 257, 337, 881, 3697, 10657, 16561, 49297, 65537, 66977, 89041, 149057, 847601, 988417, 1146097, 1972097, 2070241, 2522257, 2836961, 3553777, 3959297, 4398577, 5385761, 7166897, 11073217, 17653681, 32530177, 41532497, 44048497
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OFFSET
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1,1
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COMMENTS
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For k=1, these are the Fermat primes A019434. Is the set of generalized Fermat primes infinite? Conjecture that there are only a finite number of generalized Fermat primes for each value of k. See A077659, which shows that in cases such as k=11, there appear to be no primes. See A078901 for generalized Fermat numbers.
See A080131 for the conjectured number of primes for each k. See A080208 for the least k such that (k+1)^2^n + k^2^n is prime. The largest probable prime of this form discovered to date is the 10217-digit 312^2^12 + 311^2^12.
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LINKS
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MATHEMATICA
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lst3=Select[lst2, PrimeQ[ # ]&] (* lst2 is from A078901 *)
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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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