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A172058
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Prime numbers p such that every prime divisor of p-1 is a primitive root modulo p.
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3
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3, 5, 19, 163, 379, 419, 827, 907, 1427, 1787, 1979, 1987, 2083, 2243, 2339, 2539, 2659, 2699, 3083, 3643, 3659, 4723, 5147, 5443, 5563, 5779, 6203, 6299, 6547, 6619, 6803, 6947, 7043, 7283, 7499, 7547, 7883, 7907, 8219, 8387, 8539, 8563, 8627, 8923
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OFFSET
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1,1
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COMMENTS
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The sequence is probably infinite. If so, then there are infinitely many primes for which 2 is a primitive root (A001122).
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LINKS
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MATHEMATICA
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m = 1; s = {}; While[Prime[m] < 10000, m = m + 1; p = Prime[m]; pf = FactorInteger[p - 1]; L = Length[pf]; j = 0; While[j < L, j = j + 1; q = First[pf[[j]]]; If[MultiplicativeOrder[q, p] == p - 1, , j = L + 1]; If[j == L, s = {s, p}, ] ] ]; s = Flatten[s]
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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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