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A218834
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Primes p such that 3*p is greater than the greatest prime factor of p^3 - 1 and of p^3 + 1.
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1
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37, 47, 107, 211, 263, 373, 431, 521, 571, 631, 653, 719, 809, 821, 829, 941, 997, 1031, 1033, 1087, 1109, 1129, 1301, 1327, 1399, 1429, 1543, 1571, 1601, 1637, 1663, 1699, 1783, 1823, 1871, 1913, 1979, 1999, 2153, 2207, 2243, 2267, 2393, 2459, 2609, 2927
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OFFSET
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1,1
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LINKS
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EXAMPLE
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37^3 - 1 = 2^2*3^3*7*67, 37^3 + 1 = 2*19*31*43 and 37*3 > 43 and 37*3 > 67
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MATHEMATICA
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Select[Prime[Range[PrimePi[3000]]], 3 # > FactorInteger[#^3 - 1][[-1, 1]] && 3 # > FactorInteger[#^3 + 1][[-1, 1]] &] (* T. D. Noe, Nov 07 2012 *)
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PROG
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(PARI) forprime(h=3, 5001, for(n=3, 3, a=h^n; b=a-1; c=a+1; d=vecmax(factor(b)[, 1]~); e=vecmax(factor(c)[, 1]~); g=h*n; if(g>d && g>e, print1(h, ", "))))
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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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