
theorem
  5953 is prime
proof
  now
    5953 = 2*2976 + 1; hence not 2 divides 5953 by NAT_4:9;
    5953 = 3*1984 + 1; hence not 3 divides 5953 by NAT_4:9;
    5953 = 5*1190 + 3; hence not 5 divides 5953 by NAT_4:9;
    5953 = 7*850 + 3; hence not 7 divides 5953 by NAT_4:9;
    5953 = 11*541 + 2; hence not 11 divides 5953 by NAT_4:9;
    5953 = 13*457 + 12; hence not 13 divides 5953 by NAT_4:9;
    5953 = 17*350 + 3; hence not 17 divides 5953 by NAT_4:9;
    5953 = 19*313 + 6; hence not 19 divides 5953 by NAT_4:9;
    5953 = 23*258 + 19; hence not 23 divides 5953 by NAT_4:9;
    5953 = 29*205 + 8; hence not 29 divides 5953 by NAT_4:9;
    5953 = 31*192 + 1; hence not 31 divides 5953 by NAT_4:9;
    5953 = 37*160 + 33; hence not 37 divides 5953 by NAT_4:9;
    5953 = 41*145 + 8; hence not 41 divides 5953 by NAT_4:9;
    5953 = 43*138 + 19; hence not 43 divides 5953 by NAT_4:9;
    5953 = 47*126 + 31; hence not 47 divides 5953 by NAT_4:9;
    5953 = 53*112 + 17; hence not 53 divides 5953 by NAT_4:9;
    5953 = 59*100 + 53; hence not 59 divides 5953 by NAT_4:9;
    5953 = 61*97 + 36; hence not 61 divides 5953 by NAT_4:9;
    5953 = 67*88 + 57; hence not 67 divides 5953 by NAT_4:9;
    5953 = 71*83 + 60; hence not 71 divides 5953 by NAT_4:9;
    5953 = 73*81 + 40; hence not 73 divides 5953 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 5953 & n is prime
  holds not n divides 5953 by XPRIMET1:42;
  hence thesis by NAT_4:14;
end;
