
theorem
  5101 is prime
proof
  now
    5101 = 2*2550 + 1; hence not 2 divides 5101 by NAT_4:9;
    5101 = 3*1700 + 1; hence not 3 divides 5101 by NAT_4:9;
    5101 = 5*1020 + 1; hence not 5 divides 5101 by NAT_4:9;
    5101 = 7*728 + 5; hence not 7 divides 5101 by NAT_4:9;
    5101 = 11*463 + 8; hence not 11 divides 5101 by NAT_4:9;
    5101 = 13*392 + 5; hence not 13 divides 5101 by NAT_4:9;
    5101 = 17*300 + 1; hence not 17 divides 5101 by NAT_4:9;
    5101 = 19*268 + 9; hence not 19 divides 5101 by NAT_4:9;
    5101 = 23*221 + 18; hence not 23 divides 5101 by NAT_4:9;
    5101 = 29*175 + 26; hence not 29 divides 5101 by NAT_4:9;
    5101 = 31*164 + 17; hence not 31 divides 5101 by NAT_4:9;
    5101 = 37*137 + 32; hence not 37 divides 5101 by NAT_4:9;
    5101 = 41*124 + 17; hence not 41 divides 5101 by NAT_4:9;
    5101 = 43*118 + 27; hence not 43 divides 5101 by NAT_4:9;
    5101 = 47*108 + 25; hence not 47 divides 5101 by NAT_4:9;
    5101 = 53*96 + 13; hence not 53 divides 5101 by NAT_4:9;
    5101 = 59*86 + 27; hence not 59 divides 5101 by NAT_4:9;
    5101 = 61*83 + 38; hence not 61 divides 5101 by NAT_4:9;
    5101 = 67*76 + 9; hence not 67 divides 5101 by NAT_4:9;
    5101 = 71*71 + 60; hence not 71 divides 5101 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 5101 & n is prime
  holds not n divides 5101 by XPRIMET1:40;
  hence thesis by NAT_4:14;
end;
