
theorem
  1187 is prime
proof
  now
    1187 = 2*593 + 1; hence not 2 divides 1187 by NAT_4:9;
    1187 = 3*395 + 2; hence not 3 divides 1187 by NAT_4:9;
    1187 = 5*237 + 2; hence not 5 divides 1187 by NAT_4:9;
    1187 = 7*169 + 4; hence not 7 divides 1187 by NAT_4:9;
    1187 = 11*107 + 10; hence not 11 divides 1187 by NAT_4:9;
    1187 = 13*91 + 4; hence not 13 divides 1187 by NAT_4:9;
    1187 = 17*69 + 14; hence not 17 divides 1187 by NAT_4:9;
    1187 = 19*62 + 9; hence not 19 divides 1187 by NAT_4:9;
    1187 = 23*51 + 14; hence not 23 divides 1187 by NAT_4:9;
    1187 = 29*40 + 27; hence not 29 divides 1187 by NAT_4:9;
    1187 = 31*38 + 9; hence not 31 divides 1187 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 1187 & n is prime
  holds not n divides 1187 by XPRIMET1:22;
  hence thesis by NAT_4:14;
