
theorem
  9151 is prime
proof
  now
    9151 = 2*4575 + 1; hence not 2 divides 9151 by NAT_4:9;
    9151 = 3*3050 + 1; hence not 3 divides 9151 by NAT_4:9;
    9151 = 5*1830 + 1; hence not 5 divides 9151 by NAT_4:9;
    9151 = 7*1307 + 2; hence not 7 divides 9151 by NAT_4:9;
    9151 = 11*831 + 10; hence not 11 divides 9151 by NAT_4:9;
    9151 = 13*703 + 12; hence not 13 divides 9151 by NAT_4:9;
    9151 = 17*538 + 5; hence not 17 divides 9151 by NAT_4:9;
    9151 = 19*481 + 12; hence not 19 divides 9151 by NAT_4:9;
    9151 = 23*397 + 20; hence not 23 divides 9151 by NAT_4:9;
    9151 = 29*315 + 16; hence not 29 divides 9151 by NAT_4:9;
    9151 = 31*295 + 6; hence not 31 divides 9151 by NAT_4:9;
    9151 = 37*247 + 12; hence not 37 divides 9151 by NAT_4:9;
    9151 = 41*223 + 8; hence not 41 divides 9151 by NAT_4:9;
    9151 = 43*212 + 35; hence not 43 divides 9151 by NAT_4:9;
    9151 = 47*194 + 33; hence not 47 divides 9151 by NAT_4:9;
    9151 = 53*172 + 35; hence not 53 divides 9151 by NAT_4:9;
    9151 = 59*155 + 6; hence not 59 divides 9151 by NAT_4:9;
    9151 = 61*150 + 1; hence not 61 divides 9151 by NAT_4:9;
    9151 = 67*136 + 39; hence not 67 divides 9151 by NAT_4:9;
    9151 = 71*128 + 63; hence not 71 divides 9151 by NAT_4:9;
    9151 = 73*125 + 26; hence not 73 divides 9151 by NAT_4:9;
    9151 = 79*115 + 66; hence not 79 divides 9151 by NAT_4:9;
    9151 = 83*110 + 21; hence not 83 divides 9151 by NAT_4:9;
    9151 = 89*102 + 73; hence not 89 divides 9151 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 9151 & n is prime
  holds not n divides 9151 by XPRIMET1:48;
  hence thesis by NAT_4:14;
end;
