
theorem
  9461 is prime
proof
  now
    9461 = 2*4730 + 1; hence not 2 divides 9461 by NAT_4:9;
    9461 = 3*3153 + 2; hence not 3 divides 9461 by NAT_4:9;
    9461 = 5*1892 + 1; hence not 5 divides 9461 by NAT_4:9;
    9461 = 7*1351 + 4; hence not 7 divides 9461 by NAT_4:9;
    9461 = 11*860 + 1; hence not 11 divides 9461 by NAT_4:9;
    9461 = 13*727 + 10; hence not 13 divides 9461 by NAT_4:9;
    9461 = 17*556 + 9; hence not 17 divides 9461 by NAT_4:9;
    9461 = 19*497 + 18; hence not 19 divides 9461 by NAT_4:9;
    9461 = 23*411 + 8; hence not 23 divides 9461 by NAT_4:9;
    9461 = 29*326 + 7; hence not 29 divides 9461 by NAT_4:9;
    9461 = 31*305 + 6; hence not 31 divides 9461 by NAT_4:9;
    9461 = 37*255 + 26; hence not 37 divides 9461 by NAT_4:9;
    9461 = 41*230 + 31; hence not 41 divides 9461 by NAT_4:9;
    9461 = 43*220 + 1; hence not 43 divides 9461 by NAT_4:9;
    9461 = 47*201 + 14; hence not 47 divides 9461 by NAT_4:9;
    9461 = 53*178 + 27; hence not 53 divides 9461 by NAT_4:9;
    9461 = 59*160 + 21; hence not 59 divides 9461 by NAT_4:9;
    9461 = 61*155 + 6; hence not 61 divides 9461 by NAT_4:9;
    9461 = 67*141 + 14; hence not 67 divides 9461 by NAT_4:9;
    9461 = 71*133 + 18; hence not 71 divides 9461 by NAT_4:9;
    9461 = 73*129 + 44; hence not 73 divides 9461 by NAT_4:9;
    9461 = 79*119 + 60; hence not 79 divides 9461 by NAT_4:9;
    9461 = 83*113 + 82; hence not 83 divides 9461 by NAT_4:9;
    9461 = 89*106 + 27; hence not 89 divides 9461 by NAT_4:9;
    9461 = 97*97 + 52; hence not 97 divides 9461 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 9461 & n is prime
  holds not n divides 9461 by XPRIMET1:50;
  hence thesis by NAT_4:14;
end;
