( 426 ) 
For as 
G, — 202 XxX 198 + 27 = 202°K I & 18 tand 2% 27 P= 55 
the factor 11 might already have been pointed out in that place. 
It is evident from this, that it is desirable to investigate the factors 
of 2r +1 and of the numbers multiplied by each other. At the same 
time however non-divisors can be determined, and in this way the 
indivisibility of 383 can be proved after 6 operations, because all 
prime numbers under 1/383 have then already disappeared. Without 
omission of the non-divisors, we should have 13 operations to deal with. 
The number G = 100895598169 mentioned in the preface is im- 
mediately factorised after application of the method of remainders. 
For G = 50447799085*—50447799084?, and the root Gj of the 
subtrahend is equal to: 
224605? +. 393059 
or 224606 X 224605 + 168454, where 27 + 1 =336909. 
Kvidently Gy = 112303 is a factor and 
G=2 G,+1=2 2G, X 224605 + 3 Gy = Gy X 898423. 
Each of the factors G,—= 112303, and G; = 898423 must stil 
be dealt with. 
Gy —= 561522 — 561512 
( non-divisors ) 
r 2r 1 \minorto / Gs or 335 
56151 = 236? + 455 910 (SD 
236 x 237 + 219 439 By Mae 
235 x 238 + 221 443 47, 17 
234 & 239 + 225 450 13, 239 
233 240 + 231 463 233 
232 X 241 + 239 479 29, 241 
231 & 242 + 249 499 11 
