A057822 Smaller of pair of twin primes whose average is lcm(1,...,m) for some m.

5, 11, 59, 419, 232792559, 442720643463713815199

Offset: 1

Author

Labos Elemer, Nov 08 2000

Keywords

• nonn
• hard

Comments

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}.

No more such primes occurs below m < 2000.

No more such primes occurs below m < 30000. - Amiram Eldar, Aug 18 2024

Examples

			419 and 421 are twin primes, (419 + 421)/2 = 420 = lcm(1,2,3,4,5,6,7).
		

Crossrefs

Intersection of A057824 and {A049536(n)-2}.

Cf. A003418, A051451, A057706.

Programs

Mathematica

Select[FoldList[LCM, Select[Range[50], PrimePowerQ]] - 1, And @@ PrimeQ[# + {0, 2}] &] (* Amiram Eldar, Aug 18 2024 *)

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