
theorem
  6361 is prime
proof
  now
    6361 = 2*3180 + 1; hence not 2 divides 6361 by NAT_4:9;
    6361 = 3*2120 + 1; hence not 3 divides 6361 by NAT_4:9;
    6361 = 5*1272 + 1; hence not 5 divides 6361 by NAT_4:9;
    6361 = 7*908 + 5; hence not 7 divides 6361 by NAT_4:9;
    6361 = 11*578 + 3; hence not 11 divides 6361 by NAT_4:9;
    6361 = 13*489 + 4; hence not 13 divides 6361 by NAT_4:9;
    6361 = 17*374 + 3; hence not 17 divides 6361 by NAT_4:9;
    6361 = 19*334 + 15; hence not 19 divides 6361 by NAT_4:9;
    6361 = 23*276 + 13; hence not 23 divides 6361 by NAT_4:9;
    6361 = 29*219 + 10; hence not 29 divides 6361 by NAT_4:9;
    6361 = 31*205 + 6; hence not 31 divides 6361 by NAT_4:9;
    6361 = 37*171 + 34; hence not 37 divides 6361 by NAT_4:9;
    6361 = 41*155 + 6; hence not 41 divides 6361 by NAT_4:9;
    6361 = 43*147 + 40; hence not 43 divides 6361 by NAT_4:9;
    6361 = 47*135 + 16; hence not 47 divides 6361 by NAT_4:9;
    6361 = 53*120 + 1; hence not 53 divides 6361 by NAT_4:9;
    6361 = 59*107 + 48; hence not 59 divides 6361 by NAT_4:9;
    6361 = 61*104 + 17; hence not 61 divides 6361 by NAT_4:9;
    6361 = 67*94 + 63; hence not 67 divides 6361 by NAT_4:9;
    6361 = 71*89 + 42; hence not 71 divides 6361 by NAT_4:9;
    6361 = 73*87 + 10; hence not 73 divides 6361 by NAT_4:9;
    6361 = 79*80 + 41; hence not 79 divides 6361 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 6361 & n is prime
  holds not n divides 6361 by XPRIMET1:44;
  hence thesis by NAT_4:14;
end;
