( 336 ) 
If on the other hand we put 
N = 8573°—2?—7118 = 85758573—7118 
= 5°X T8573 —2 3559, 
N = 8573°—3?—7113 = 85768570—7113 
= 216110851 —.38 X 2371, 
N = 8577X8569—7106 = 9X953x11K19K41—2 XU X17TX19, 
then MN appears to be divisible by 11 and 19, but not by 8573, 
3940, 61, 851, 2571," 953, 41-17. 
The series 7121, 7118, 7113, 7106, ete. of the numbers c shows 
the differences 3, 5, 7, etc. if a is increased and 06 diminished 
by unity. 
The division having been achieved, we find as quotient 
N, = 351623 = 593?—26, with 13 (factor of 26) as non-divisor. 
By means of 14 operations already 23 of the 106 prime numbers 
minor to /N can be declared to be non-divisors; by testing 47 
and 61 by direct division all divisors minor to 71 are shut out. 
NIN? (NIN? 
If we put N= (—=) — ( 3 ) , at least one of the two suc- 
1 oe eae a 
cessive numbers and oe divisible by 2 or 3 or 2 X 3. 
The divisors of the quotient so obtained are non-divisors of N. 
IV. Determination of the difference of the factors. 
We put a=b + m and therefore N= (6 + m)? — b? = m(m + 25). 
Now we try to determine 5 and m by assuming for m a value near 
IN? 8 
aie 
to /N, ‘calculating N?—m? and then 26 = 
quotient be not an entire number we repeat this calculation with 
an m smaller by two (m being odd with A). 
(To be continued.) 
