
theorem
  5051 is prime
proof
  now
    5051 = 2*2525 + 1; hence not 2 divides 5051 by NAT_4:9;
    5051 = 3*1683 + 2; hence not 3 divides 5051 by NAT_4:9;
    5051 = 5*1010 + 1; hence not 5 divides 5051 by NAT_4:9;
    5051 = 7*721 + 4; hence not 7 divides 5051 by NAT_4:9;
    5051 = 11*459 + 2; hence not 11 divides 5051 by NAT_4:9;
    5051 = 13*388 + 7; hence not 13 divides 5051 by NAT_4:9;
    5051 = 17*297 + 2; hence not 17 divides 5051 by NAT_4:9;
    5051 = 19*265 + 16; hence not 19 divides 5051 by NAT_4:9;
    5051 = 23*219 + 14; hence not 23 divides 5051 by NAT_4:9;
    5051 = 29*174 + 5; hence not 29 divides 5051 by NAT_4:9;
    5051 = 31*162 + 29; hence not 31 divides 5051 by NAT_4:9;
    5051 = 37*136 + 19; hence not 37 divides 5051 by NAT_4:9;
    5051 = 41*123 + 8; hence not 41 divides 5051 by NAT_4:9;
    5051 = 43*117 + 20; hence not 43 divides 5051 by NAT_4:9;
    5051 = 47*107 + 22; hence not 47 divides 5051 by NAT_4:9;
    5051 = 53*95 + 16; hence not 53 divides 5051 by NAT_4:9;
    5051 = 59*85 + 36; hence not 59 divides 5051 by NAT_4:9;
    5051 = 61*82 + 49; hence not 61 divides 5051 by NAT_4:9;
    5051 = 67*75 + 26; hence not 67 divides 5051 by NAT_4:9;
    5051 = 71*71 + 10; hence not 71 divides 5051 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 5051 & n is prime
  holds not n divides 5051 by XPRIMET1:40;
  hence thesis by NAT_4:14;
end;
