
theorem
  7057 is prime
proof
  now
    7057 = 2*3528 + 1; hence not 2 divides 7057 by NAT_4:9;
    7057 = 3*2352 + 1; hence not 3 divides 7057 by NAT_4:9;
    7057 = 5*1411 + 2; hence not 5 divides 7057 by NAT_4:9;
    7057 = 7*1008 + 1; hence not 7 divides 7057 by NAT_4:9;
    7057 = 11*641 + 6; hence not 11 divides 7057 by NAT_4:9;
    7057 = 13*542 + 11; hence not 13 divides 7057 by NAT_4:9;
    7057 = 17*415 + 2; hence not 17 divides 7057 by NAT_4:9;
    7057 = 19*371 + 8; hence not 19 divides 7057 by NAT_4:9;
    7057 = 23*306 + 19; hence not 23 divides 7057 by NAT_4:9;
    7057 = 29*243 + 10; hence not 29 divides 7057 by NAT_4:9;
    7057 = 31*227 + 20; hence not 31 divides 7057 by NAT_4:9;
    7057 = 37*190 + 27; hence not 37 divides 7057 by NAT_4:9;
    7057 = 41*172 + 5; hence not 41 divides 7057 by NAT_4:9;
    7057 = 43*164 + 5; hence not 43 divides 7057 by NAT_4:9;
    7057 = 47*150 + 7; hence not 47 divides 7057 by NAT_4:9;
    7057 = 53*133 + 8; hence not 53 divides 7057 by NAT_4:9;
    7057 = 59*119 + 36; hence not 59 divides 7057 by NAT_4:9;
    7057 = 61*115 + 42; hence not 61 divides 7057 by NAT_4:9;
    7057 = 67*105 + 22; hence not 67 divides 7057 by NAT_4:9;
    7057 = 71*99 + 28; hence not 71 divides 7057 by NAT_4:9;
    7057 = 73*96 + 49; hence not 73 divides 7057 by NAT_4:9;
    7057 = 79*89 + 26; hence not 79 divides 7057 by NAT_4:9;
    7057 = 83*85 + 2; hence not 83 divides 7057 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 7057 & n is prime
  holds not n divides 7057 by XPRIMET1:46;
  hence thesis by NAT_4:14;
end;
