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A088256
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Primorial numbers k such that both k-1 and k+1 are prime.
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4
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OFFSET
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1,1
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COMMENTS
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Conjecture: sequence is finite.
Search extended to first 3000 primorials. - Josey Stevens, Aug 10 2021
The first more than 230000 primorial numbers k have been checked for whether k-1 or k+1 or both are primes. See links. If another term k exists, it is over about 10^1400000. - Jeppe Stig Nielsen, Oct 19 2021
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LINKS
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EXAMPLE
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210 = primorial(4) is not a member as 209 is composite.
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MAPLE
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f:= proc(n)
local P;
P:= mul(seq(ithprime(i), i=1..n));
if isprime(P+1) and isprime(P-1) then P else NULL fi
end proc:
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MATHEMATICA
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Select[Times @@ # & /@ Prime@ Range@ Range@ 700, Times @@ Boole@ PrimeQ@ {# - 1, # + 1} == 1 &] (* Michael De Vlieger, Aug 31 2016 *)
Select[FoldList[Times, Prime[Range[20]]], AllTrue[#+{1, -1}, PrimeQ]&] (* Harvey P. Dale, Mar 31 2023 *)
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PROG
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(PARI) lista(nn) = for (n=1, nn, pr = prod(i=1, n, prime(i)); if (isprime(pr-1) && isprime(pr+1), print1(pr, ", "))); \\ Michel Marcus, Aug 31 2016
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CROSSREFS
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KEYWORD
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more,nonn,bref
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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