
theorem
  5867 is prime
proof
  now
    5867 = 2*2933 + 1; hence not 2 divides 5867 by NAT_4:9;
    5867 = 3*1955 + 2; hence not 3 divides 5867 by NAT_4:9;
    5867 = 5*1173 + 2; hence not 5 divides 5867 by NAT_4:9;
    5867 = 7*838 + 1; hence not 7 divides 5867 by NAT_4:9;
    5867 = 11*533 + 4; hence not 11 divides 5867 by NAT_4:9;
    5867 = 13*451 + 4; hence not 13 divides 5867 by NAT_4:9;
    5867 = 17*345 + 2; hence not 17 divides 5867 by NAT_4:9;
    5867 = 19*308 + 15; hence not 19 divides 5867 by NAT_4:9;
    5867 = 23*255 + 2; hence not 23 divides 5867 by NAT_4:9;
    5867 = 29*202 + 9; hence not 29 divides 5867 by NAT_4:9;
    5867 = 31*189 + 8; hence not 31 divides 5867 by NAT_4:9;
    5867 = 37*158 + 21; hence not 37 divides 5867 by NAT_4:9;
    5867 = 41*143 + 4; hence not 41 divides 5867 by NAT_4:9;
    5867 = 43*136 + 19; hence not 43 divides 5867 by NAT_4:9;
    5867 = 47*124 + 39; hence not 47 divides 5867 by NAT_4:9;
    5867 = 53*110 + 37; hence not 53 divides 5867 by NAT_4:9;
    5867 = 59*99 + 26; hence not 59 divides 5867 by NAT_4:9;
    5867 = 61*96 + 11; hence not 61 divides 5867 by NAT_4:9;
    5867 = 67*87 + 38; hence not 67 divides 5867 by NAT_4:9;
    5867 = 71*82 + 45; hence not 71 divides 5867 by NAT_4:9;
    5867 = 73*80 + 27; hence not 73 divides 5867 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 5867 & n is prime
  holds not n divides 5867 by XPRIMET1:42;
  hence thesis by NAT_4:14;
end;
