
theorem
  5869 is prime
proof
  now
    5869 = 2*2934 + 1; hence not 2 divides 5869 by NAT_4:9;
    5869 = 3*1956 + 1; hence not 3 divides 5869 by NAT_4:9;
    5869 = 5*1173 + 4; hence not 5 divides 5869 by NAT_4:9;
    5869 = 7*838 + 3; hence not 7 divides 5869 by NAT_4:9;
    5869 = 11*533 + 6; hence not 11 divides 5869 by NAT_4:9;
    5869 = 13*451 + 6; hence not 13 divides 5869 by NAT_4:9;
    5869 = 17*345 + 4; hence not 17 divides 5869 by NAT_4:9;
    5869 = 19*308 + 17; hence not 19 divides 5869 by NAT_4:9;
    5869 = 23*255 + 4; hence not 23 divides 5869 by NAT_4:9;
    5869 = 29*202 + 11; hence not 29 divides 5869 by NAT_4:9;
    5869 = 31*189 + 10; hence not 31 divides 5869 by NAT_4:9;
    5869 = 37*158 + 23; hence not 37 divides 5869 by NAT_4:9;
    5869 = 41*143 + 6; hence not 41 divides 5869 by NAT_4:9;
    5869 = 43*136 + 21; hence not 43 divides 5869 by NAT_4:9;
    5869 = 47*124 + 41; hence not 47 divides 5869 by NAT_4:9;
    5869 = 53*110 + 39; hence not 53 divides 5869 by NAT_4:9;
    5869 = 59*99 + 28; hence not 59 divides 5869 by NAT_4:9;
    5869 = 61*96 + 13; hence not 61 divides 5869 by NAT_4:9;
    5869 = 67*87 + 40; hence not 67 divides 5869 by NAT_4:9;
    5869 = 71*82 + 47; hence not 71 divides 5869 by NAT_4:9;
    5869 = 73*80 + 29; hence not 73 divides 5869 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 5869 & n is prime
  holds not n divides 5869 by XPRIMET1:42;
  hence thesis by NAT_4:14;
end;
