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%I #37 Apr 03 2023 10:36:12
%S 2,3,23,8641,653184001,
%T 1601591599167888308924824752807936000000000000001
%N Primes p such that p + 1 or p - 1 is in A066120.
%C What is the next prime? As of January 2012, there are no known primes ending in 9 with this property.
%H G. L. Honaker, Jr. and Chris Caldwell, <a href="https://t5k.org/curios/cpage/24439.html">Prime Curios! 8641</a>
%F a(n) are the prime values of p(0)# * (p(0)# * p(1)#) * (p(0)# * p(1)# * p(2)#) * (p(0)# * p(1)# * p(2)# * ... * p(n)#) +/- 1.
%e A002110(1)^3*A002110(2)^2*A002110(3) + 1 = 8641, which is prime.
%t Select[Flatten[Table[Product[Product[Product[Prime[i], {i, j}], {j, k}], {k, n}] - 1 + m, {n, 0, 7}, {m, 0, 2, 2}]], PrimeQ]
%Y Cf. A066120, A002110.
%K hard,nonn
%O 1,1
%A _Arkadiusz Wesolowski_, Jan 06 2012
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