
theorem
  7187 is prime
proof
  now
    7187 = 2*3593 + 1; hence not 2 divides 7187 by NAT_4:9;
    7187 = 3*2395 + 2; hence not 3 divides 7187 by NAT_4:9;
    7187 = 5*1437 + 2; hence not 5 divides 7187 by NAT_4:9;
    7187 = 7*1026 + 5; hence not 7 divides 7187 by NAT_4:9;
    7187 = 11*653 + 4; hence not 11 divides 7187 by NAT_4:9;
    7187 = 13*552 + 11; hence not 13 divides 7187 by NAT_4:9;
    7187 = 17*422 + 13; hence not 17 divides 7187 by NAT_4:9;
    7187 = 19*378 + 5; hence not 19 divides 7187 by NAT_4:9;
    7187 = 23*312 + 11; hence not 23 divides 7187 by NAT_4:9;
    7187 = 29*247 + 24; hence not 29 divides 7187 by NAT_4:9;
    7187 = 31*231 + 26; hence not 31 divides 7187 by NAT_4:9;
    7187 = 37*194 + 9; hence not 37 divides 7187 by NAT_4:9;
    7187 = 41*175 + 12; hence not 41 divides 7187 by NAT_4:9;
    7187 = 43*167 + 6; hence not 43 divides 7187 by NAT_4:9;
    7187 = 47*152 + 43; hence not 47 divides 7187 by NAT_4:9;
    7187 = 53*135 + 32; hence not 53 divides 7187 by NAT_4:9;
    7187 = 59*121 + 48; hence not 59 divides 7187 by NAT_4:9;
    7187 = 61*117 + 50; hence not 61 divides 7187 by NAT_4:9;
    7187 = 67*107 + 18; hence not 67 divides 7187 by NAT_4:9;
    7187 = 71*101 + 16; hence not 71 divides 7187 by NAT_4:9;
    7187 = 73*98 + 33; hence not 73 divides 7187 by NAT_4:9;
    7187 = 79*90 + 77; hence not 79 divides 7187 by NAT_4:9;
    7187 = 83*86 + 49; hence not 83 divides 7187 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 7187 & n is prime
  holds not n divides 7187 by XPRIMET1:46;
  hence thesis by NAT_4:14;
end;
