Factorization of "aba"

Abstract - What is "aba" ?

"aba" is a number of the following form,

aba(a,b,n) = aba...aba = ((10a+b)*10(2n+1)-(a+10b))/99
where b is not equal to a.

For example, in case of '191',

191
19191
1919191
...

This data is a good touchstone for SNFS.

Factors of "aba"

• a=1..9, b=1..9 (where b is not equal to a)
• n=1..100
• All numbers were checked with ECM-GMP, B1=5e4, 240 curves, B1=25e4, 500 curves and B1=1e6, 1100 curves
aba factorslast updateremaining
12is equal to 133..331/11, see near rep-digit numbers
3is equal to 144..441/11, see near rep-digit numbers
4is equal to 155..551/11, see near rep-digit numbers
5is equal to 166..661/11, see near rep-digit numbers
6is equal to 177..771/11, see near rep-digit numbers
7is equal to 188..881/11, see near rep-digit numbers
8is equal to 199..991/11, see near rep-digit numbers
9Sep. 16, 20128
21Apr. 18, 20094
3Jan 19, 200910
4is equal to 121..121 * 2, see aba(1,2,n)
5Mar. 09, 200910
6is equal to 131..131 * 2, see aba(1,3,n)
7Nov. 03, 200811
8is equal to 141..141 * 2, see aba(1,4,n)
9Aug. 30, 20097
31is equal to 344..443/11, see near rep-digit numbers
2is equal to 355..553/11, see near rep-digit numbers
4is equal to 377..773/11, see near rep-digit numbers
5is equal to 388..881/11, see near rep-digit numbers
6is equal to 121..121 * 3, see aba(1,2,n)
7Jul. 13, 20098
8Jul. 29, 20096
9is equal to 131..131 * 3, see aba(1,3,n)
41Mar. 21, 20096
2is equal to 212..212 * 2, see aba(2,1,n)
3Nov. 10, 20087
5Oct. 10, 20088
6is equal to 232..232 * 2, see aba(2,3,n)
7Dec. 08, 20088
8is equal to 121..121 * 4, see aba(1,2,n)
9Dec. 01, 20089
51Nov. 10, 20089
2Jun. 14, 20094
3Sep. 08, 20085
4Jun. 02, 20088
6Mar. 21, 200910
7Jul. 02, 20098
8Sep. 12, 20096
9Apr. 13, 20099
61Jun. 20, 20095
2is equal to 313..313 * 2, see aba(3,1,n)
3is equal to 212..212 * 3, see aba(2,1,n)
4is equal to 323..323 * 2, see aba(3,2,n)
5Feb. 16, 20097
7Aug. 09, 20096
8is equal to 343..343 * 2, see aba(3,4,n)
9is equal to 232..232 * 3, see aba(2,3,n)
71is equal to 788..887/11, see near rep-digit numbers
2is equal to 799..997/11, see near rep-digit numbers
3Oct. 04, 20087
4Sep. 08, 200811
5Apr. 26, 20098
6Jan. 12, 20096
8May 12, 20099
9Feb. 09, 20098
81Mar. 16, 200910
2is equal to 414..414 * 2, see aba(4,1,n)
3Dec. 30, 20087
4is equal to 212..212 * 4, see aba(2,1,n)
5Sep. 01, 20086
6is equal to 434..434 * 2, see aba(4,3,n)
7Jul. 28, 20083
9Jun. 01, 20098
91Jul. 18, 20097
2May 21, 20095
3is equal to 313..313 * 3, see aba(3,1,n)
4Oct. 10, 20088
5Jul. 29, 20096
6is equal to 323..323 * 3, see aba(3,2,n)
7Feb. 23, 20095
8Jan. 30, 20097

E-mail : kc2h-msm@asahi-net.or.jp
Hisanori Mishima