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A348307
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Primes p such that (p-1)/2, (p-2)/3, 2*p+1, 3*p+2 are all prime numbers.
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0
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23, 21383, 26459, 28643, 111263, 137339, 217643, 333563, 342599, 423323, 486023, 540539, 548519, 567719, 658943, 671039, 755663, 829463, 865499, 890063, 903803, 976883, 1108259, 1168523, 1199183, 1308383, 1316699, 1318379, 1342403, 1349423, 1390199, 1501583, 1503059, 1558079, 1563119
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OFFSET
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1,1
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COMMENTS
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For (p-1)/2, those are the safe primes A005385.
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LINKS
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EXAMPLE
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23 is a term because: (23-1)/2 = 11, (23-2)/3 = 7, 2*23+1 = 47, 3*23+2 = 71, {23, 11, 7, 47, 71} are all prime numbers.
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MATHEMATICA
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Select[Range[1, 1.5*10^6, 2], AllTrue[{#, (# - 1)/2, (# - 2)/3, 2*# + 1, 3*# + 2}, PrimeQ] &] (* Amiram Eldar, Oct 11 2021 *)
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PROG
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(PARI) isok(p) = iferr(isprime(p) && isprime((p-1)/2) && isprime((p-2)/3) && isprime(2*p+1) && isprime(3*p+2), E, 0); \\ Michel Marcus, Oct 11 2021
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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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