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A221982
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Primes p == 2 (mod 5) for which 4*p+1 is also prime.
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2
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7, 37, 67, 97, 127, 277, 307, 487, 577, 727, 997, 1087, 1297, 1327, 1567, 1597, 1777, 1987, 2017, 2437, 2647, 2677, 2767, 2887, 3037, 3067, 3307, 3457, 3637, 3907, 4057, 4297, 4447, 4567, 4987, 5197, 5527, 5557, 6007, 6247, 6337, 6367, 6397, 6547, 6577, 7027, 7057, 7237, 7417, 7507, 7717, 7867
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OFFSET
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1,1
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COMMENTS
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The corresponding primes 4*p+1 are Chebyshev's subsequence A221981 of the primes with primitive root 10.
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REFERENCES
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P. L. Chebyshev, Theory of congruences. Elements of number theory, Chelsea, 1972, p. 306.
R. K. Guy, Unsolved Problems in Number Theory, F9.
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LINKS
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FORMULA
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EXAMPLE
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7 is a member because 7 == 2 (mod 5) and 29 = 4*7 + 1 are both prime.
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MAPLE
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local n;
for n from 1 to q do
if isprime(n) and isprime(4*n+1) and (n mod 5)=2 then print(n) fi; od; end:
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MATHEMATICA
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Select[ Prime[ Range[1000]], Mod[#, 5] == 2 && PrimeQ[4 # + 1] &]
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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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