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%I #27 Aug 18 2024 04:17:03
%S 5,11,59,419,232792559,442720643463713815199
%N Smaller of pair of twin primes whose average is lcm(1,...,m) for some m.
%C Known values of m such that lcm(1,...,m) is a twin prime mean value are as follows: {3, 4, 5, 6, 7, 19, 20, 21, 22, 47, 48}.
%C No more such primes occurs below m < 2000.
%C No more such primes occurs below m < 30000. - _Amiram Eldar_, Aug 18 2024
%e 419 and 421 are twin primes, (419 + 421)/2 = 420 = lcm(1,2,3,4,5,6,7).
%t Select[FoldList[LCM, Select[Range[50], PrimePowerQ]] - 1, And @@ PrimeQ[# + {0, 2}] &] (* _Amiram Eldar_, Aug 18 2024 *)
%o (PARI) lista(nn=50) = {for (i=1, nn, if (isprimepower(i), if (isprime(p=lcm([2..i])-1) && isprime(p+2), print1(p, ", "));););} \\ _Michel Marcus_, Aug 25 2019
%Y Intersection of A057824 and {A049536(n)-2}.
%Y Cf. A003418, A051451, A057706.
%K nonn,hard
%O 1,1
%A _Labos Elemer_, Nov 08 2000