
theorem
  5749 is prime
proof
  now
    5749 = 2*2874 + 1; hence not 2 divides 5749 by NAT_4:9;
    5749 = 3*1916 + 1; hence not 3 divides 5749 by NAT_4:9;
    5749 = 5*1149 + 4; hence not 5 divides 5749 by NAT_4:9;
    5749 = 7*821 + 2; hence not 7 divides 5749 by NAT_4:9;
    5749 = 11*522 + 7; hence not 11 divides 5749 by NAT_4:9;
    5749 = 13*442 + 3; hence not 13 divides 5749 by NAT_4:9;
    5749 = 17*338 + 3; hence not 17 divides 5749 by NAT_4:9;
    5749 = 19*302 + 11; hence not 19 divides 5749 by NAT_4:9;
    5749 = 23*249 + 22; hence not 23 divides 5749 by NAT_4:9;
    5749 = 29*198 + 7; hence not 29 divides 5749 by NAT_4:9;
    5749 = 31*185 + 14; hence not 31 divides 5749 by NAT_4:9;
    5749 = 37*155 + 14; hence not 37 divides 5749 by NAT_4:9;
    5749 = 41*140 + 9; hence not 41 divides 5749 by NAT_4:9;
    5749 = 43*133 + 30; hence not 43 divides 5749 by NAT_4:9;
    5749 = 47*122 + 15; hence not 47 divides 5749 by NAT_4:9;
    5749 = 53*108 + 25; hence not 53 divides 5749 by NAT_4:9;
    5749 = 59*97 + 26; hence not 59 divides 5749 by NAT_4:9;
    5749 = 61*94 + 15; hence not 61 divides 5749 by NAT_4:9;
    5749 = 67*85 + 54; hence not 67 divides 5749 by NAT_4:9;
    5749 = 71*80 + 69; hence not 71 divides 5749 by NAT_4:9;
    5749 = 73*78 + 55; hence not 73 divides 5749 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 5749 & n is prime
  holds not n divides 5749 by XPRIMET1:42;
  hence thesis by NAT_4:14;
end;
