
theorem
  5881 is prime
proof
  now
    5881 = 2*2940 + 1; hence not 2 divides 5881 by NAT_4:9;
    5881 = 3*1960 + 1; hence not 3 divides 5881 by NAT_4:9;
    5881 = 5*1176 + 1; hence not 5 divides 5881 by NAT_4:9;
    5881 = 7*840 + 1; hence not 7 divides 5881 by NAT_4:9;
    5881 = 11*534 + 7; hence not 11 divides 5881 by NAT_4:9;
    5881 = 13*452 + 5; hence not 13 divides 5881 by NAT_4:9;
    5881 = 17*345 + 16; hence not 17 divides 5881 by NAT_4:9;
    5881 = 19*309 + 10; hence not 19 divides 5881 by NAT_4:9;
    5881 = 23*255 + 16; hence not 23 divides 5881 by NAT_4:9;
    5881 = 29*202 + 23; hence not 29 divides 5881 by NAT_4:9;
    5881 = 31*189 + 22; hence not 31 divides 5881 by NAT_4:9;
    5881 = 37*158 + 35; hence not 37 divides 5881 by NAT_4:9;
    5881 = 41*143 + 18; hence not 41 divides 5881 by NAT_4:9;
    5881 = 43*136 + 33; hence not 43 divides 5881 by NAT_4:9;
    5881 = 47*125 + 6; hence not 47 divides 5881 by NAT_4:9;
    5881 = 53*110 + 51; hence not 53 divides 5881 by NAT_4:9;
    5881 = 59*99 + 40; hence not 59 divides 5881 by NAT_4:9;
    5881 = 61*96 + 25; hence not 61 divides 5881 by NAT_4:9;
    5881 = 67*87 + 52; hence not 67 divides 5881 by NAT_4:9;
    5881 = 71*82 + 59; hence not 71 divides 5881 by NAT_4:9;
    5881 = 73*80 + 41; hence not 73 divides 5881 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 5881 & n is prime
  holds not n divides 5881 by XPRIMET1:42;
  hence thesis by NAT_4:14;
end;
