
theorem
  5981 is prime
proof
  now
    5981 = 2*2990 + 1; hence not 2 divides 5981 by NAT_4:9;
    5981 = 3*1993 + 2; hence not 3 divides 5981 by NAT_4:9;
    5981 = 5*1196 + 1; hence not 5 divides 5981 by NAT_4:9;
    5981 = 7*854 + 3; hence not 7 divides 5981 by NAT_4:9;
    5981 = 11*543 + 8; hence not 11 divides 5981 by NAT_4:9;
    5981 = 13*460 + 1; hence not 13 divides 5981 by NAT_4:9;
    5981 = 17*351 + 14; hence not 17 divides 5981 by NAT_4:9;
    5981 = 19*314 + 15; hence not 19 divides 5981 by NAT_4:9;
    5981 = 23*260 + 1; hence not 23 divides 5981 by NAT_4:9;
    5981 = 29*206 + 7; hence not 29 divides 5981 by NAT_4:9;
    5981 = 31*192 + 29; hence not 31 divides 5981 by NAT_4:9;
    5981 = 37*161 + 24; hence not 37 divides 5981 by NAT_4:9;
    5981 = 41*145 + 36; hence not 41 divides 5981 by NAT_4:9;
    5981 = 43*139 + 4; hence not 43 divides 5981 by NAT_4:9;
    5981 = 47*127 + 12; hence not 47 divides 5981 by NAT_4:9;
    5981 = 53*112 + 45; hence not 53 divides 5981 by NAT_4:9;
    5981 = 59*101 + 22; hence not 59 divides 5981 by NAT_4:9;
    5981 = 61*98 + 3; hence not 61 divides 5981 by NAT_4:9;
    5981 = 67*89 + 18; hence not 67 divides 5981 by NAT_4:9;
    5981 = 71*84 + 17; hence not 71 divides 5981 by NAT_4:9;
    5981 = 73*81 + 68; hence not 73 divides 5981 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 5981 & n is prime
  holds not n divides 5981 by XPRIMET1:42;
  hence thesis by NAT_4:14;
end;
