3847 = (2 * 1923) + 1 ;
hence not 2 divides 3847 by NAT_4:9; :: thesis:
3847 = (3 * 1282) + 1 ;
hence not 3 divides 3847 by NAT_4:9; :: thesis:
3847 = (5 * 769) + 2 ;
hence not 5 divides 3847 by NAT_4:9; :: thesis:
3847 = (7 * 549) + 4 ;
hence not 7 divides 3847 by NAT_4:9; :: thesis:
3847 = (11 * 349) + 8 ;
hence not 11 divides 3847 by NAT_4:9; :: thesis:
3847 = (13 * 295) + 12 ;
hence not 13 divides 3847 by NAT_4:9; :: thesis:
3847 = (17 * 226) + 5 ;
hence not 17 divides 3847 by NAT_4:9; :: thesis:
3847 = (19 * 202) + 9 ;
hence not 19 divides 3847 by NAT_4:9; :: thesis:
3847 = (23 * 167) + 6 ;
hence not 23 divides 3847 by NAT_4:9; :: thesis:
3847 = (29 * 132) + 19 ;
hence not 29 divides 3847 by NAT_4:9; :: thesis:
3847 = (31 * 124) + 3 ;
hence not 31 divides 3847 by NAT_4:9; :: thesis:
3847 = (37 * 103) + 36 ;
hence not 37 divides 3847 by NAT_4:9; :: thesis:
3847 = (41 * 93) + 34 ;
hence not 41 divides 3847 by NAT_4:9; :: thesis:
3847 = (43 * 89) + 20 ;
hence not 43 divides 3847 by NAT_4:9; :: thesis:
3847 = (47 * 81) + 40 ;
hence not 47 divides 3847 by NAT_4:9; :: thesis:
3847 = (53 * 72) + 31 ;
hence not 53 divides 3847 by NAT_4:9; :: thesis:
3847 = (59 * 65) + 12 ;
hence not 59 divides 3847 by NAT_4:9; :: thesis:
3847 = (61 * 63) + 4 ;
hence not 61 divides 3847 by NAT_4:9; :: thesis:

end;

then for n being Element of NAT st 1 < n & n * n <= 3847 & n is prime holds
not n divides 3847 by XPRIMET1:36;
hence 3847 is prime by NAT_4:14; :: thesis: