3907 = (2 * 1953) + 1 ;
hence not 2 divides 3907 by NAT_4:9; :: thesis:
3907 = (3 * 1302) + 1 ;
hence not 3 divides 3907 by NAT_4:9; :: thesis:
3907 = (5 * 781) + 2 ;
hence not 5 divides 3907 by NAT_4:9; :: thesis:
3907 = (7 * 558) + 1 ;
hence not 7 divides 3907 by NAT_4:9; :: thesis:
3907 = (11 * 355) + 2 ;
hence not 11 divides 3907 by NAT_4:9; :: thesis:
3907 = (13 * 300) + 7 ;
hence not 13 divides 3907 by NAT_4:9; :: thesis:
3907 = (17 * 229) + 14 ;
hence not 17 divides 3907 by NAT_4:9; :: thesis:
3907 = (19 * 205) + 12 ;
hence not 19 divides 3907 by NAT_4:9; :: thesis:
3907 = (23 * 169) + 20 ;
hence not 23 divides 3907 by NAT_4:9; :: thesis:
3907 = (29 * 134) + 21 ;
hence not 29 divides 3907 by NAT_4:9; :: thesis:
3907 = (31 * 126) + 1 ;
hence not 31 divides 3907 by NAT_4:9; :: thesis:
3907 = (37 * 105) + 22 ;
hence not 37 divides 3907 by NAT_4:9; :: thesis:
3907 = (41 * 95) + 12 ;
hence not 41 divides 3907 by NAT_4:9; :: thesis:
3907 = (43 * 90) + 37 ;
hence not 43 divides 3907 by NAT_4:9; :: thesis:
3907 = (47 * 83) + 6 ;
hence not 47 divides 3907 by NAT_4:9; :: thesis:
3907 = (53 * 73) + 38 ;
hence not 53 divides 3907 by NAT_4:9; :: thesis:
3907 = (59 * 66) + 13 ;
hence not 59 divides 3907 by NAT_4:9; :: thesis:
3907 = (61 * 64) + 3 ;
hence not 61 divides 3907 by NAT_4:9; :: thesis:

end;

then for n being Element of NAT st 1 < n & n * n <= 3907 & n is prime holds
not n divides 3907 by XPRIMET1:36;
hence 3907 is prime by NAT_4:14; :: thesis: