A173935 a(n) is the least prime that is the concatenation of two primes in exactly n different ways.
2, 23, 313, 3137, 233347, 739397, 379837313, 73932013313, 7399973479337
Offset: 0
Examples
23 = 2 & 3, 313 = 3 & 13 and 31 & 3, etc.
Programs
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Mathematica
f[n_] := Block[{c = 0, id = IntegerDigits@n, k = 0}, len = Length@ id; While[ k < len, If[ Union@ PrimeQ[ FromDigits@# & /@ {id[[;; k + 1]], id[[k + 2 ;;]]}] == {True}, c++ ]; k++ ]; c]; t = Table[0, {10}]; p = 2; While[p < 10^8, a = f@p; If[ t[[a]] == 0, t[[a]] = p; Print[{a, p}]]; p = NextPrime@ p]
Extensions
a(6) from Robert G. Wilson v, Mar 04 2010
a(7) from Donovan Johnson, Nov 09 2010
a(8) from Giovanni Resta, Mar 04 2014