A343706 Lesser emirps (A109308) p such that A056964(p) is in A343703.

17, 107, 113, 167, 179, 389, 1031, 1091, 1097, 1109, 1181, 1259, 1439, 1487, 1523, 1583, 1619, 1847, 3023, 3089, 3257, 3347, 3359, 3527, 3719, 7349, 7529, 7577, 7589, 7649, 7949, 9029, 10067, 10151, 10247, 10487, 10739, 10781, 11057, 11423, 11621, 11777, 11897, 11933, 12119, 12227, 12641, 13151

Offset: 1

Author

J. M. Bergot and Robert Israel, Apr 26 2021

Keywords

• nonn
• base

Comments

Primes p such that the digit-reversal q = A004086(p) is a prime greater than p, and p+q = x*y for some x and y such that x+y and the concatenation x|y are primes.

Examples

			a(4) = 167 is a term because 167 and 761 are primes with 167 < 761, and 167+761 = 928 = 32*29 with 3229 and 32+29 = 61 prime.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000
• Carlos Rivera, Puzzle 1036. P + R(p) such that..., The Prime Puzzles and Problems Connection.

Crossrefs

Cf. A004086, A056964, A109308, A343703.

Programs

Maple

revdigs:= proc(n) local L,i;
    L:= convert(n,base,10);
    add(L[-i]*10^(i-1),i=1..nops(L))
end proc:
filter:= proc(p) local q,m,d,e;
   q:= revdigs(p); if q <= p then return false fi;
   if not isprime(p) or not isprime(q) then return false fi;
   m:= p+q;
   for d in numtheory:-divisors(m) do
     e:= m/d;
     if isprime(d*10^(1+ilog10(e))+e) and isprime(d+e) then return true fi
   od;
   false
end proc: