
theorem
  5641 is prime
proof
  now
    5641 = 2*2820 + 1; hence not 2 divides 5641 by NAT_4:9;
    5641 = 3*1880 + 1; hence not 3 divides 5641 by NAT_4:9;
    5641 = 5*1128 + 1; hence not 5 divides 5641 by NAT_4:9;
    5641 = 7*805 + 6; hence not 7 divides 5641 by NAT_4:9;
    5641 = 11*512 + 9; hence not 11 divides 5641 by NAT_4:9;
    5641 = 13*433 + 12; hence not 13 divides 5641 by NAT_4:9;
    5641 = 17*331 + 14; hence not 17 divides 5641 by NAT_4:9;
    5641 = 19*296 + 17; hence not 19 divides 5641 by NAT_4:9;
    5641 = 23*245 + 6; hence not 23 divides 5641 by NAT_4:9;
    5641 = 29*194 + 15; hence not 29 divides 5641 by NAT_4:9;
    5641 = 31*181 + 30; hence not 31 divides 5641 by NAT_4:9;
    5641 = 37*152 + 17; hence not 37 divides 5641 by NAT_4:9;
    5641 = 41*137 + 24; hence not 41 divides 5641 by NAT_4:9;
    5641 = 43*131 + 8; hence not 43 divides 5641 by NAT_4:9;
    5641 = 47*120 + 1; hence not 47 divides 5641 by NAT_4:9;
    5641 = 53*106 + 23; hence not 53 divides 5641 by NAT_4:9;
    5641 = 59*95 + 36; hence not 59 divides 5641 by NAT_4:9;
    5641 = 61*92 + 29; hence not 61 divides 5641 by NAT_4:9;
    5641 = 67*84 + 13; hence not 67 divides 5641 by NAT_4:9;
    5641 = 71*79 + 32; hence not 71 divides 5641 by NAT_4:9;
    5641 = 73*77 + 20; hence not 73 divides 5641 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 5641 & n is prime
  holds not n divides 5641 by XPRIMET1:42;
  hence thesis by NAT_4:14;
end;
