
theorem
  5669 is prime
proof
  now
    5669 = 2*2834 + 1; hence not 2 divides 5669 by NAT_4:9;
    5669 = 3*1889 + 2; hence not 3 divides 5669 by NAT_4:9;
    5669 = 5*1133 + 4; hence not 5 divides 5669 by NAT_4:9;
    5669 = 7*809 + 6; hence not 7 divides 5669 by NAT_4:9;
    5669 = 11*515 + 4; hence not 11 divides 5669 by NAT_4:9;
    5669 = 13*436 + 1; hence not 13 divides 5669 by NAT_4:9;
    5669 = 17*333 + 8; hence not 17 divides 5669 by NAT_4:9;
    5669 = 19*298 + 7; hence not 19 divides 5669 by NAT_4:9;
    5669 = 23*246 + 11; hence not 23 divides 5669 by NAT_4:9;
    5669 = 29*195 + 14; hence not 29 divides 5669 by NAT_4:9;
    5669 = 31*182 + 27; hence not 31 divides 5669 by NAT_4:9;
    5669 = 37*153 + 8; hence not 37 divides 5669 by NAT_4:9;
    5669 = 41*138 + 11; hence not 41 divides 5669 by NAT_4:9;
    5669 = 43*131 + 36; hence not 43 divides 5669 by NAT_4:9;
    5669 = 47*120 + 29; hence not 47 divides 5669 by NAT_4:9;
    5669 = 53*106 + 51; hence not 53 divides 5669 by NAT_4:9;
    5669 = 59*96 + 5; hence not 59 divides 5669 by NAT_4:9;
    5669 = 61*92 + 57; hence not 61 divides 5669 by NAT_4:9;
    5669 = 67*84 + 41; hence not 67 divides 5669 by NAT_4:9;
    5669 = 71*79 + 60; hence not 71 divides 5669 by NAT_4:9;
    5669 = 73*77 + 48; hence not 73 divides 5669 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 5669 & n is prime
  holds not n divides 5669 by XPRIMET1:42;
  hence thesis by NAT_4:14;
end;
