
theorem
  5197 is prime
proof
  now
    5197 = 2*2598 + 1; hence not 2 divides 5197 by NAT_4:9;
    5197 = 3*1732 + 1; hence not 3 divides 5197 by NAT_4:9;
    5197 = 5*1039 + 2; hence not 5 divides 5197 by NAT_4:9;
    5197 = 7*742 + 3; hence not 7 divides 5197 by NAT_4:9;
    5197 = 11*472 + 5; hence not 11 divides 5197 by NAT_4:9;
    5197 = 13*399 + 10; hence not 13 divides 5197 by NAT_4:9;
    5197 = 17*305 + 12; hence not 17 divides 5197 by NAT_4:9;
    5197 = 19*273 + 10; hence not 19 divides 5197 by NAT_4:9;
    5197 = 23*225 + 22; hence not 23 divides 5197 by NAT_4:9;
    5197 = 29*179 + 6; hence not 29 divides 5197 by NAT_4:9;
    5197 = 31*167 + 20; hence not 31 divides 5197 by NAT_4:9;
    5197 = 37*140 + 17; hence not 37 divides 5197 by NAT_4:9;
    5197 = 41*126 + 31; hence not 41 divides 5197 by NAT_4:9;
    5197 = 43*120 + 37; hence not 43 divides 5197 by NAT_4:9;
    5197 = 47*110 + 27; hence not 47 divides 5197 by NAT_4:9;
    5197 = 53*98 + 3; hence not 53 divides 5197 by NAT_4:9;
    5197 = 59*88 + 5; hence not 59 divides 5197 by NAT_4:9;
    5197 = 61*85 + 12; hence not 61 divides 5197 by NAT_4:9;
    5197 = 67*77 + 38; hence not 67 divides 5197 by NAT_4:9;
    5197 = 71*73 + 14; hence not 71 divides 5197 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 5197 & n is prime
  holds not n divides 5197 by XPRIMET1:40;
  hence thesis by NAT_4:14;
end;
