Meeting Report April 2019

Factoring Large Numbers. Bob B.

Bob showed his number program (mp) which was written in C but uses 'curses' under Linux. This gives a pseudo-graphical interface with scrolling windows, but outputs as normal ASCII characters.

It is mainly used for factorizing numbers, but can produce many number patterns easily without typing in every digit.

For example, the number (10^101 - 1)/9 gives a 101-digit number consisting of all ones (11111...111). It was then factorized into three large factors using the program.

Here is the result:

W = 11,111,111,111,111,111,111,111,111,111,111,111,111,111,111,111,111,111,111,111,111,111,111,111,111,111,111,111,111,111,111,111,111,111 - 101

Mp: 36

Ecm, B1 = 10,000

Ecm, B1 = 2,120,000 211 (16:06|10)

elapsed time 00:16:06

V = 4,531,530,181,816,613,234,555,190,841 - 28 ==> p28.C73

S = Not saved

W = 2,451,955,667,358,449,766,574,244,930,742,726,059,038,594,502,086,245,442,706,362,842,197,225,471 - 73

Mp: 37

Msieve - 73 digits

prp33 factor: 129063282232848961951985354966759

prp41 factor: 18998088572819375252842078421374368604969

elapsed time 00:01:26

V = 129,063,282,232,848,961,951,985,354,966,759 - 33 ==> p33.p41

S = Not saved

W = 18,998,088,572,819,375,252,842,078,421,374,368,604,969 - 41

Mp:

This shows that the first factor was found in 16 mins and 6 secs, but the second only took 1 min and 26 secs.

The final result is:

N = 4,531,530,181,816,613,234,555,190,841 (28-digits) *

129,063,282,232,848,961,951,985,354,966,759 (33-digits) *

18,998,088,572,819,375,252,842,078,421,374,368,604,969 (41-digits)

An interesting pastime."

Home Lab and Development Boards. Anthony B.

See attached pdf file.