A374669 a(n) is the least number with n prime factors (counted with multiplicity) that is the concatenation of two primes.

23, 22, 27, 132, 32, 729, 192, 2112, 1792, 5632, 3072, 59392, 64512, 90112, 110592, 950272, 2260992, 3244032, 786432, 30277632, 7340032, 23068672, 12582912, 494927872, 1333788672, 1375731712, 704643072, 3892314112, 1879048192, 37446746112, 27380416512, 196494753792, 30064771072, 94489280512

Offset: 1

Author

Robert Israel, Jul 15 2024

Keywords

• nonn
• base

Examples

			a(4) = 132 because 132 = 2^2 * 3 * 11 is the product of 4 primes (counted with multiplicity) and is the concatenation of the two primes 13 and 2.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A001222. Second column of A374376.

Programs

Maple

cp:= proc(n) local k;
  if n::even then n mod 10 = 2 and isprime((n-2)/10)
  elif n mod 5 = 0 then isprime((n-5)/10)
  else for k from 1 to ilog10(n) do
    if isprime(n mod 10^k) and isprime(floor(n/10^k)) then return true fi
    od;
    false
  fi
end proc:
f:= proc(n) uses priqueue; local pq, p, q, T, TP, j, v;
  initialize(pq);
  insert([-2^n,2$n],pq);
  do
    T:= extract(pq);
    v:= -T[1];
    if cp(v) then return(v) fi;
    q:= T[-1];
    p:= nextprime(q);
    for j from n+1 to 2 by -1 do
      if T[j] <> q then break fi;
      TP:= [T[1]*(p/q)^(n+2-j), op(T[2..j-1]), p$(n+2-j)];
      insert(TP, pq)
  od od;
end proc:
map(f, [$1..30]);