
theorem
  5807 is prime
proof
  now
    5807 = 2*2903 + 1; hence not 2 divides 5807 by NAT_4:9;
    5807 = 3*1935 + 2; hence not 3 divides 5807 by NAT_4:9;
    5807 = 5*1161 + 2; hence not 5 divides 5807 by NAT_4:9;
    5807 = 7*829 + 4; hence not 7 divides 5807 by NAT_4:9;
    5807 = 11*527 + 10; hence not 11 divides 5807 by NAT_4:9;
    5807 = 13*446 + 9; hence not 13 divides 5807 by NAT_4:9;
    5807 = 17*341 + 10; hence not 17 divides 5807 by NAT_4:9;
    5807 = 19*305 + 12; hence not 19 divides 5807 by NAT_4:9;
    5807 = 23*252 + 11; hence not 23 divides 5807 by NAT_4:9;
    5807 = 29*200 + 7; hence not 29 divides 5807 by NAT_4:9;
    5807 = 31*187 + 10; hence not 31 divides 5807 by NAT_4:9;
    5807 = 37*156 + 35; hence not 37 divides 5807 by NAT_4:9;
    5807 = 41*141 + 26; hence not 41 divides 5807 by NAT_4:9;
    5807 = 43*135 + 2; hence not 43 divides 5807 by NAT_4:9;
    5807 = 47*123 + 26; hence not 47 divides 5807 by NAT_4:9;
    5807 = 53*109 + 30; hence not 53 divides 5807 by NAT_4:9;
    5807 = 59*98 + 25; hence not 59 divides 5807 by NAT_4:9;
    5807 = 61*95 + 12; hence not 61 divides 5807 by NAT_4:9;
    5807 = 67*86 + 45; hence not 67 divides 5807 by NAT_4:9;
    5807 = 71*81 + 56; hence not 71 divides 5807 by NAT_4:9;
    5807 = 73*79 + 40; hence not 73 divides 5807 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 5807 & n is prime
  holds not n divides 5807 by XPRIMET1:42;
  hence thesis by NAT_4:14;
end;
