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A101996
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Primes of the form 8*k-1 such that 4*k-1, 16*k-1, 32*k-1 and 64*k-1 are also primes.
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8
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359, 107279, 126839, 253679, 254279, 508559, 592199, 681839, 1214639, 1621079, 2138399, 2245319, 3197399, 3243239, 3641999, 3732479, 3825359, 3841919, 4090679, 4276799, 4315799, 4490639, 4556159, 4714439, 5335559, 5731679
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OFFSET
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1,1
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LINKS
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FORMULA
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EXAMPLE
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4*45-1 = 179, 8*45-1 = 359, 16*45-1 = 719, 32*45-1 = 1439 and 64*45-1 = 2879 are primes, so 359 is a term.
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MATHEMATICA
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8#-1&/@Select[Range[720000], AllTrue[{4, 8, 16, 32, 64}#-1, PrimeQ]&] (* Harvey P. Dale, Jan 17 2023 *)
Select[Table[2^Range[2, 6] n-1, {n, 750000}], AllTrue[#, PrimeQ]&][[;; , 2]] (* Harvey P. Dale, Jun 03 2023 *)
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PROG
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(PARI) is(k) = if(k % 8 == 7, my(m = k\8 + 1); isprime(4*m-1) && isprime(8*m-1) && isprime(16*m-1) && isprime(32*m-1) && isprime(64*m-1), 0); \\ Amiram Eldar, May 13 2024
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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Douglas Stones (dssto1(AT)student.monash.edu.au), Dec 23 2004
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EXTENSIONS
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STATUS
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approved
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