
theorem
  5209 is prime
proof
  now
    5209 = 2*2604 + 1; hence not 2 divides 5209 by NAT_4:9;
    5209 = 3*1736 + 1; hence not 3 divides 5209 by NAT_4:9;
    5209 = 5*1041 + 4; hence not 5 divides 5209 by NAT_4:9;
    5209 = 7*744 + 1; hence not 7 divides 5209 by NAT_4:9;
    5209 = 11*473 + 6; hence not 11 divides 5209 by NAT_4:9;
    5209 = 13*400 + 9; hence not 13 divides 5209 by NAT_4:9;
    5209 = 17*306 + 7; hence not 17 divides 5209 by NAT_4:9;
    5209 = 19*274 + 3; hence not 19 divides 5209 by NAT_4:9;
    5209 = 23*226 + 11; hence not 23 divides 5209 by NAT_4:9;
    5209 = 29*179 + 18; hence not 29 divides 5209 by NAT_4:9;
    5209 = 31*168 + 1; hence not 31 divides 5209 by NAT_4:9;
    5209 = 37*140 + 29; hence not 37 divides 5209 by NAT_4:9;
    5209 = 41*127 + 2; hence not 41 divides 5209 by NAT_4:9;
    5209 = 43*121 + 6; hence not 43 divides 5209 by NAT_4:9;
    5209 = 47*110 + 39; hence not 47 divides 5209 by NAT_4:9;
    5209 = 53*98 + 15; hence not 53 divides 5209 by NAT_4:9;
    5209 = 59*88 + 17; hence not 59 divides 5209 by NAT_4:9;
    5209 = 61*85 + 24; hence not 61 divides 5209 by NAT_4:9;
    5209 = 67*77 + 50; hence not 67 divides 5209 by NAT_4:9;
    5209 = 71*73 + 26; hence not 71 divides 5209 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 5209 & n is prime
  holds not n divides 5209 by XPRIMET1:40;
  hence thesis by NAT_4:14;
end;
