
theorem
  7127 is prime
proof
  now
    7127 = 2*3563 + 1; hence not 2 divides 7127 by NAT_4:9;
    7127 = 3*2375 + 2; hence not 3 divides 7127 by NAT_4:9;
    7127 = 5*1425 + 2; hence not 5 divides 7127 by NAT_4:9;
    7127 = 7*1018 + 1; hence not 7 divides 7127 by NAT_4:9;
    7127 = 11*647 + 10; hence not 11 divides 7127 by NAT_4:9;
    7127 = 13*548 + 3; hence not 13 divides 7127 by NAT_4:9;
    7127 = 17*419 + 4; hence not 17 divides 7127 by NAT_4:9;
    7127 = 19*375 + 2; hence not 19 divides 7127 by NAT_4:9;
    7127 = 23*309 + 20; hence not 23 divides 7127 by NAT_4:9;
    7127 = 29*245 + 22; hence not 29 divides 7127 by NAT_4:9;
    7127 = 31*229 + 28; hence not 31 divides 7127 by NAT_4:9;
    7127 = 37*192 + 23; hence not 37 divides 7127 by NAT_4:9;
    7127 = 41*173 + 34; hence not 41 divides 7127 by NAT_4:9;
    7127 = 43*165 + 32; hence not 43 divides 7127 by NAT_4:9;
    7127 = 47*151 + 30; hence not 47 divides 7127 by NAT_4:9;
    7127 = 53*134 + 25; hence not 53 divides 7127 by NAT_4:9;
    7127 = 59*120 + 47; hence not 59 divides 7127 by NAT_4:9;
    7127 = 61*116 + 51; hence not 61 divides 7127 by NAT_4:9;
    7127 = 67*106 + 25; hence not 67 divides 7127 by NAT_4:9;
    7127 = 71*100 + 27; hence not 71 divides 7127 by NAT_4:9;
    7127 = 73*97 + 46; hence not 73 divides 7127 by NAT_4:9;
    7127 = 79*90 + 17; hence not 79 divides 7127 by NAT_4:9;
    7127 = 83*85 + 72; hence not 83 divides 7127 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 7127 & n is prime
  holds not n divides 7127 by XPRIMET1:46;
  hence thesis by NAT_4:14;
end;
