
theorem
  5927 is prime
proof
  now
    5927 = 2*2963 + 1; hence not 2 divides 5927 by NAT_4:9;
    5927 = 3*1975 + 2; hence not 3 divides 5927 by NAT_4:9;
    5927 = 5*1185 + 2; hence not 5 divides 5927 by NAT_4:9;
    5927 = 7*846 + 5; hence not 7 divides 5927 by NAT_4:9;
    5927 = 11*538 + 9; hence not 11 divides 5927 by NAT_4:9;
    5927 = 13*455 + 12; hence not 13 divides 5927 by NAT_4:9;
    5927 = 17*348 + 11; hence not 17 divides 5927 by NAT_4:9;
    5927 = 19*311 + 18; hence not 19 divides 5927 by NAT_4:9;
    5927 = 23*257 + 16; hence not 23 divides 5927 by NAT_4:9;
    5927 = 29*204 + 11; hence not 29 divides 5927 by NAT_4:9;
    5927 = 31*191 + 6; hence not 31 divides 5927 by NAT_4:9;
    5927 = 37*160 + 7; hence not 37 divides 5927 by NAT_4:9;
    5927 = 41*144 + 23; hence not 41 divides 5927 by NAT_4:9;
    5927 = 43*137 + 36; hence not 43 divides 5927 by NAT_4:9;
    5927 = 47*126 + 5; hence not 47 divides 5927 by NAT_4:9;
    5927 = 53*111 + 44; hence not 53 divides 5927 by NAT_4:9;
    5927 = 59*100 + 27; hence not 59 divides 5927 by NAT_4:9;
    5927 = 61*97 + 10; hence not 61 divides 5927 by NAT_4:9;
    5927 = 67*88 + 31; hence not 67 divides 5927 by NAT_4:9;
    5927 = 71*83 + 34; hence not 71 divides 5927 by NAT_4:9;
    5927 = 73*81 + 14; hence not 73 divides 5927 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 5927 & n is prime
  holds not n divides 5927 by XPRIMET1:42;
  hence thesis by NAT_4:14;
end;
