
theorem
  3697 is prime
proof
  now
    3697 = 2*1848 + 1; hence not 2 divides 3697 by NAT_4:9;
    3697 = 3*1232 + 1; hence not 3 divides 3697 by NAT_4:9;
    3697 = 5*739 + 2; hence not 5 divides 3697 by NAT_4:9;
    3697 = 7*528 + 1; hence not 7 divides 3697 by NAT_4:9;
    3697 = 11*336 + 1; hence not 11 divides 3697 by NAT_4:9;
    3697 = 13*284 + 5; hence not 13 divides 3697 by NAT_4:9;
    3697 = 17*217 + 8; hence not 17 divides 3697 by NAT_4:9;
    3697 = 19*194 + 11; hence not 19 divides 3697 by NAT_4:9;
    3697 = 23*160 + 17; hence not 23 divides 3697 by NAT_4:9;
    3697 = 29*127 + 14; hence not 29 divides 3697 by NAT_4:9;
    3697 = 31*119 + 8; hence not 31 divides 3697 by NAT_4:9;
    3697 = 37*99 + 34; hence not 37 divides 3697 by NAT_4:9;
    3697 = 41*90 + 7; hence not 41 divides 3697 by NAT_4:9;
    3697 = 43*85 + 42; hence not 43 divides 3697 by NAT_4:9;
    3697 = 47*78 + 31; hence not 47 divides 3697 by NAT_4:9;
    3697 = 53*69 + 40; hence not 53 divides 3697 by NAT_4:9;
    3697 = 59*62 + 39; hence not 59 divides 3697 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 3697 & n is prime
  holds not n divides 3697 by XPRIMET1:34;
  hence thesis by NAT_4:14;
end;
