%I #8 Apr 03 2023 10:36:11

%S 373,11311,17971,37273,37573,39293,71317,93739,97379,1193911,1317131,

%T 1371731,1793971,3166613,3319133,3337333,3479743,3716173,3722273,

%U 3763673,3769673,3774773,3792973,3793973,3799973,3916193,7118117

%N Palindromic primes with d digits which have more than 3*d/2 distinct primes as substrings, for any d > 0.

%C The prime itself and its prime digits are counted among the prime substrings.

%H C. Caldwell, G.L. Honaker (Editors), <a href="https://t5k.org/curios/page.php?short=13151715131">Prime curios!: 13151715131</a>, by _M. F. Hasler_, Nov. 2009.

%e The prime 13151715131 is in the sequence since it is palindromic, of length 11, and contains the following 17 > 11*3/2 distinct primes as substrings: 3, 5, 7, 13, 17, 31, 71, 131, 151, 5171, 7151, 13151, 15131, 31517, 517151, 1315171513 and 13151715131.

%o (PARI) prime_substrings(p) = { p=Vec(Str(p)); select( x->isprime(x), vecsort( concat( vector( #p,i, vector( i,j, eval( concat( vecextract( p, Str(j".."i))))))),8))} /* Note: In PARI version 2.4.2 (dvt CHANGES-1.1971), the syntax is select(L,f) instead of select(f,L). */

%o {forprime( p=2,default(primelimit), p==eval(concat(vecextract(Vec(Str(p)),"-1..1")))|next; #prime_substrings(p) > #Str(p)*3\2 & print1(p", "))}

%K base,nonn

%O 1,1

%A _M. F. Hasler_, Nov 23 2009