
theorem
  5897 is prime
proof
  now
    5897 = 2*2948 + 1; hence not 2 divides 5897 by NAT_4:9;
    5897 = 3*1965 + 2; hence not 3 divides 5897 by NAT_4:9;
    5897 = 5*1179 + 2; hence not 5 divides 5897 by NAT_4:9;
    5897 = 7*842 + 3; hence not 7 divides 5897 by NAT_4:9;
    5897 = 11*536 + 1; hence not 11 divides 5897 by NAT_4:9;
    5897 = 13*453 + 8; hence not 13 divides 5897 by NAT_4:9;
    5897 = 17*346 + 15; hence not 17 divides 5897 by NAT_4:9;
    5897 = 19*310 + 7; hence not 19 divides 5897 by NAT_4:9;
    5897 = 23*256 + 9; hence not 23 divides 5897 by NAT_4:9;
    5897 = 29*203 + 10; hence not 29 divides 5897 by NAT_4:9;
    5897 = 31*190 + 7; hence not 31 divides 5897 by NAT_4:9;
    5897 = 37*159 + 14; hence not 37 divides 5897 by NAT_4:9;
    5897 = 41*143 + 34; hence not 41 divides 5897 by NAT_4:9;
    5897 = 43*137 + 6; hence not 43 divides 5897 by NAT_4:9;
    5897 = 47*125 + 22; hence not 47 divides 5897 by NAT_4:9;
    5897 = 53*111 + 14; hence not 53 divides 5897 by NAT_4:9;
    5897 = 59*99 + 56; hence not 59 divides 5897 by NAT_4:9;
    5897 = 61*96 + 41; hence not 61 divides 5897 by NAT_4:9;
    5897 = 67*88 + 1; hence not 67 divides 5897 by NAT_4:9;
    5897 = 71*83 + 4; hence not 71 divides 5897 by NAT_4:9;
    5897 = 73*80 + 57; hence not 73 divides 5897 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 5897 & n is prime
  holds not n divides 5897 by XPRIMET1:42;
  hence thesis by NAT_4:14;
end;
