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A330304
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Prime numbers P such that Q=2*P-1, R=4*Q+1, S=6*R+1, T=8*S-1, U=10*T+1 and V=12*U-1 are all prime numbers.
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1
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2, 34057, 36847, 207997, 612967, 11035807, 14015167, 19251097, 19587577, 25602547, 26953957, 28060717, 29722177, 29808277, 32894437, 40874857, 41691607, 49713127, 53064877, 54539827, 69143017, 85320577, 101516137, 110327797, 110712247, 123088117, 131584417, 140028607, 150780517
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OFFSET
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1,1
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COMMENTS
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P, Q, R, S, T, U, V are 7 primes in near-geometric progression (2, 4, 6, 8, 10, 12 plus or minus one) starting P = a(n).
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LINKS
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EXAMPLE
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2*2-1=3, 4*3+1=13, 6*13+1=79, 8*79-1=631, 10*631+1=6311, 12*6311-1=75731, where 2, 3, 13, 79, 631, 6311 and 75731 are all prime numbers; so 2 is the first term.
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PROG
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(PARI) forprime(P=2, 130000000, my(Q=2*P-1, R=4*Q+1, S=6*R+1, T=8*S-1, U=10*T+1, V=12*U-1); if(isprime(Q)&&isprime(R)&&isprime(S)&&isprime(T)&&isprime(U)&&isprime(V), print1(P, ", "))) \\ Hugo Pfoertner, Dec 17 2019
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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