
theorem
  5879 is prime
proof
  now
    5879 = 2*2939 + 1; hence not 2 divides 5879 by NAT_4:9;
    5879 = 3*1959 + 2; hence not 3 divides 5879 by NAT_4:9;
    5879 = 5*1175 + 4; hence not 5 divides 5879 by NAT_4:9;
    5879 = 7*839 + 6; hence not 7 divides 5879 by NAT_4:9;
    5879 = 11*534 + 5; hence not 11 divides 5879 by NAT_4:9;
    5879 = 13*452 + 3; hence not 13 divides 5879 by NAT_4:9;
    5879 = 17*345 + 14; hence not 17 divides 5879 by NAT_4:9;
    5879 = 19*309 + 8; hence not 19 divides 5879 by NAT_4:9;
    5879 = 23*255 + 14; hence not 23 divides 5879 by NAT_4:9;
    5879 = 29*202 + 21; hence not 29 divides 5879 by NAT_4:9;
    5879 = 31*189 + 20; hence not 31 divides 5879 by NAT_4:9;
    5879 = 37*158 + 33; hence not 37 divides 5879 by NAT_4:9;
    5879 = 41*143 + 16; hence not 41 divides 5879 by NAT_4:9;
    5879 = 43*136 + 31; hence not 43 divides 5879 by NAT_4:9;
    5879 = 47*125 + 4; hence not 47 divides 5879 by NAT_4:9;
    5879 = 53*110 + 49; hence not 53 divides 5879 by NAT_4:9;
    5879 = 59*99 + 38; hence not 59 divides 5879 by NAT_4:9;
    5879 = 61*96 + 23; hence not 61 divides 5879 by NAT_4:9;
    5879 = 67*87 + 50; hence not 67 divides 5879 by NAT_4:9;
    5879 = 71*82 + 57; hence not 71 divides 5879 by NAT_4:9;
    5879 = 73*80 + 39; hence not 73 divides 5879 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 5879 & n is prime
  holds not n divides 5879 by XPRIMET1:42;
  hence thesis by NAT_4:14;
end;
