A121608 Primes that can be written as concatenation of two composite numbers in decimal representation.

89, 109, 149, 229, 269, 349, 359, 389, 409, 421, 433, 439, 449, 457, 463, 487, 491, 499, 509, 569, 659, 677, 691, 709, 769, 809, 821, 827, 829, 839, 857, 859, 863, 877, 881, 887, 919, 929, 977, 991, 1009, 1021, 1033, 1039, 1049, 1051, 1063, 1069, 1087, 1091

Offset: 1

Author

Reinhard Zumkeller, Aug 10 2006

Keywords

• nonn
• base

Examples

			A000040(169) = 1009 = 100*10+9 = A002808(74)*10+A002808(4), therefore 1009 is a term: a(41) = 1009;
A000040(172) = 1021 = 10*100+21 = A002808(5)*100+A002808(12), therefore 1021 is a term: a(42) = 1021.
		

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A105184, A121609, A121610.

Programs

Python

from sympy import isprime
def comp(s): i=int(s); return s[0]!='0' and i > 1 and not isprime(i)
def ok(n):
  s = str(n)
  for i in range(1, len(s)):
    if comp(s[:i]) and comp(s[i:]) and isprime(int(s)): return True
print([m for m in range(1092) if ok(m)]) # Michael S. Branicky, Feb 27 2021