Operation: Billion Digits
I'd like for some people to join me in the quest for both a billiondigit prime and $250,000. From the benchmarks and Prime95, I found the lowest prime (just the exponent obviously) in this category was M3321928097. I'd like to have someone start off by advanced factoring it. You should probably do 50 bits. Please reply if you want to take this exponent. But be sure to specify the amount of bits you are factoring with. You me also post comments if necessary.

2^3321928097  1
6643856195 is the starting factor .......................................! 6158854691839 is a FACTOR of 2^3321928097  1 k*2*p + 1 927*2*3321928097 + 1 
Next canidates: 3321928109, 3321928121, 3321928171

[QUOTE=Uncwilly]Next canidates: 3321928109, 3321928121, 3321928171[/QUOTE]
408676883681617 divides 2^3321928109 408676883681617 = 61512*2*p+1 
[QUOTE=Uncwilly]Next canidates: 3321928109, 3321928121, 3321928171[/QUOTE]
684317192927 divides 2^33219281211 684317192927 = 103*2*p+1 
[QUOTE=wblipp]684317192927 divides 2^33219281211
684317192927 = 103*2*p+1[/QUOTE] 3,321,928,171 no factor up to 60.033 bits, k=179,309,108 Luigi 
[QUOTE=ET_]3,321,928,171 no factor up to 60.033 bits, k=179,309,108
Luigi[/QUOTE] Factorization of 3,321,928,097  3,321,928,109 and 3,321,928,121 taken up to 60 bits. Here is the results file [CODE] M3321928097 has a factor: 6158854691839 M3321928097 has a factor: 41457662650561 M3321928109 has a factor: 408676883681617 M3321928121 has a factor: 684317192927 M3321928121 has a factor: 502959849088127 [/CODE] All factors will be sent to Will Edgington if no other did it. Luigi 
Just wondering. Does anyone know how many P90 CPU Hours are needed to LL test an exponent, n (as a function of n)?

Doubling the exponent results in at least four times the execution time.

So, a billion exponent would take a time that is equivalent to ~25,000 2^20,996,0111 tests??? Wow. :surrender

[QUOTE=Nuri]So, a billion exponent would take a time that is equivalent to ~25,000 2^20,996,0111 tests??? Wow. :surrender[/QUOTE]
The LL test is actually O(N[sup]2[/sup]logN), since it is an O(NlogN) FFT multiply performed N times. Accounting for the extra term, it would take ~32,000 times the time it took to test M40. For numbers of this size, it makes much more sense to use numbers which can be tested using Proth's theorem, allowing many numbers with almost exactly 1 billion digits to be tested, instead of being forced to test larger and larger Mersenne numbers. 
So the LL test does not win the "race to infinity" for finding ever larger primes (compared to other methods)?

[QUOTE=jinydu]So the LL test does not win the "race to infinity" for finding ever larger primes (compared to other methods)?[/QUOTE]
LL, proth, generalized fermat are all O(n^2 log n). The LL test has the smallest constant. Let's say that the LL test is 1.5 times as fast as the generalized fermat, and 4 times faster than the proth test. Your best algorithm to find a billion digit prime is then: 1) search for a 1 to 1.5 billion digit Mersenne prime. If none found: 2) start searching for billion digit generalized fermats too. 3) If you get to 4 billion digit Mersenne numbers and 2.6 billion digit generalized fermat numbers and still haven't found a prime, then start searching for billion digit Proth primes too. 
So if there are no Mersenne Primes with less than 1.5 billiion digits, it is the best thing to search for generalized fermat primes, becasue there are pleny of them. you can just square the basis and half the exponent, and the searching field gets much bigger.
If we estimate about 1000 cpu years on a average P4 for a single test, and a chance of 1 in 300Million I doubt that it is worth the electricity just for the price. But the fascination in that is somewhere else. 
[QUOTE=jinydu]So the LL test does not win the "race to infinity" for finding ever larger primes (compared to other methods)?[/QUOTE]
(another reply) No, the LL test always wins, compared to other methods, for [u]samesized numbers[/u]. But there are only three or four Mersenne numbers (not to mention that most have composite exponents) in any given range denoted by a certain number of decimal digits, whereas there are millions and millions of exactly1,000,000,000digit nonMersenne primes waiting to be discovered by methods other than LL. Then, as one extends LL testing to Mersenne numbers of more than 1,000,000,000 digits, the time required gets longer, and eventually exceeds the time required for a nonLL test of a 1,000,000,000digit nonMersenne number. After one factors in the differing predicted densities of primes, one finds a tradeoff point at which it's more costeffective to switch to an asymptotically slower method on smaller numbers. 
So if I ask for a prime with at least n digits in as small a time as possible, which method should I use as n approaches infinity?

[QUOTE=ET_]3,321,928,171 no factor up to 60.033 bits, k=179,309,108
Luigi[/QUOTE] Will you be taking this any further? Did you use your own program? William 
[QUOTE=wblipp]Will you be taking this any further? Did you use your own program?
William[/QUOTE] How about we have one person Advanced P1 it while another Advanced ECM 100 curves? If that doesn't work, someone could factor about 118 bits. We'll figure it out after that. :unsure: LLs would take 852 years, 209 days, 1 hours, 27 minutes for that exponent! 
[QUOTE=clowns789]How about we have one person Advanced P1 it while another Advanced ECM 100 curves? If that doesn't work, someone could factor about 118 bits.[/QUOTE]
Can we really do anything except trial factor? P1, P+1, and ECM all perform calculations modulo the billion digit number  I thought that would be a problem. Trial factoring requires calculations modulo the trial factor  a much smaller number. Will Prime95 AdvancedFactor work this large? It didn't work my machine. I think Luigi was using his own program. I was using Excel with the Zmath addin. William 
[QUOTE=wblipp]Will you be taking this any further? Did you use your own program?
William[/QUOTE] I used my program. If you think it could be useful, I will go further, just tell me the bitdepth you need (just remember my program is far slower than Prime95...) :smile: Luigi 
[QUOTE=ET_]I used my program. If you think it could be useful, I will go further, [/QUOTE]
[I]Useful?[/I] That's a pretty strong standard. Operation Billion Digits is a Children's Crusade, needing fifteentwenty years of continuing Moore's Law before the LL test becomes feasible. I thought it would be fun to continue a while further, though. And the only paths I see to advance Project Billion Digits are to advance the trial factoring of this candidate or to trial factor some other candidates. [QUOTE=ET_]just remember my program is far slower than Prime95[/QUOTE] What methods are you using to filter the k values before determining 2kp+1? We only need to test prime values of 2kp+1, so various sieving methods are possible. In my Excel spreadsheet I used a wheel of size 13# to automatically avoid k values where 2kp+1 had any divisors 13 or less, but larger wheels and/or other methods could make sense in a C program. In the spreadsheet, I noticed that occasionally the value of mod(2^p, 2kp+1) was a power of 2, and this leads to other Mersenne factors. You might want to consider checking for these possibilities and saving the results for later processing. 
Can you modify Prime95 source code? Perhaps it could be 23.9.

[QUOTE=wblipp]
What methods are you using to filter the k values before determining 2kp+1? We only need to test prime values of 2kp+1, so various sieving methods are possible. [/QUOTE] I'm checking factors mod 120 instead of 1 or 7 mod 8, and apply primality checking up to (around) 7000. Checking for higher factors would slow subsequent modulo operations on the Mersenne number even if it gets a higher number of K sieved out.. I am still working on source code to translate it into English and eliminate debug calls. Two people have already asked me for the source, if you are interested I can send it to you also. Meanwhile I will take the range of 3,321,928,171 a bit (or two...) further. Finally, I would like to thank Andreas Pipp's work (Andi314): he prompted me towards the right path with his program using Crandall libraries. Luigi 
3,321,928,171 no factor up to 63.001 bits, k=1,391,351,436
Going up to 67 bits... BTW, I also wrote a version of the program that accepts a batch textfile with exponents and startend bits... Luigi 
[QUOTE=ET_]I also wrote a version of the program that accepts a batch textfile with exponents and startend bits...
Luigi[/QUOTE] Sorry for the autoquote... editing is disabled :unsure: I mean, we may have a batch of "billion" exponents and try them up to (say) 58 bits to gather some more fators and play with them. Luigi 
[QUOTE=ET_]3,321,928,171 no factor up to 63.001 bits, k=1,391,351,436
Going up to 67 bits... [/QUOTE] The next two primes have easy factors M( 3321928189 )C: 312261249767 M( 3321928189 )C: 43284724302671 M( 3321928217 )C: 1166521668825287 But M(3321928217) is also stubborn. If you send the program, I'll start a machine on trial factoring this one. William 
Should be:
But M(332192821[b]9[/b]) is also stubborn. If you send the program, I'll start a machine on trial factoring this one. William 
3,321,928,171 no factor up to 66.034 bits, k>11,000,000,000
Still going up to 67 bits... and working with an old 250 MHz PII. William, I'll repost my program as soon as I implement a stronger resuming algorithm (by the end of the week) Luigi 
[QUOTE=ET_]William, I'll repost my program as soon as I implement a stronger resuming algorithm (by the end of the week)
Luigi[/QUOTE] And here it is :smile: Many thanks to Nick Fortino who implemented a trick to gain another 5% of speed :banana: Factor3_1 now can use the r switch to resume from his status.txt file. Now a question: I have a batch version of this program, and a list of about 3300 prime exponents starting from 3321928241,1,50 and ending with 3321999991,1,50 to feed it. We could start a *real* "Billion Project", sieving those exponents up to 50 bits, sending factors to Will Edgington and factoring deeper the tough ones. I could coordinate the ranges and the found factors. We won't find any prime number this way, but projects starting in the next 10 years will have to use our farseeing effort :flex: Is anybody interested in this work? Luigi 
1 Attachment(s)
[QUOTE=ET_]And here it is :smile: [/QUOTE]
I say HERE it is. Due to a small glith in the previous version, here is the REAL one to download. Xyzzy may you please cancel the file attached to the previous post? :innocent: Luigi 
[code]
M3321928171 no factor from 2^61 to 2^67. [/code] Luigi 
[QUOTE=ET_]I could coordinate the ranges and the found factors. We won't find any prime number this way, but projects starting in the next 10 years will have to use our farseeing effort :flex:[/QUOTE]You could work this with the >79.3M LMH project if you want, let me know and we'll make you a comod over there...

[QUOTE=Xyzzy]You could work this with the >79.3M LMH project if you want, let me know and we'll make you a comod over there...[/QUOTE]
That sounds great! I guess someone has the full list of found exponents, their factors and their bit depth... we could accomodate the results on a web page. :lol: Luigi 
[QUOTE=ET_]
Now a question: I have a batch version of this program, and a list of about 3300 prime exponents starting from 3321928241,1,50 and ending with 3321999991,1,50 to feed it.[/QUOTE] I'm attracted by the whimsical nature of starting a project that there is no hope of finishing. But not sufficiently attracted to put serious computing power towards it. I envision using an old PentiumPro 180 to gradually advance a single exponent. If there is no objection, I'll work on 3321928219. William 
[QUOTE=wblipp]I'm attracted by the whimsical nature of starting a project that there is no hope of finishing. But not sufficiently attracted to put serious computing power towards it. I envision using an old PentiumPro 180 to gradually advance a single exponent. If there is no objection, I'll work on 3321928219.
William[/QUOTE] That's OK for me. Then I will comoderate LMH > 79,2 Project, eventually giving a small boost to the search :smile: Luigi 
[QUOTE=ET_]I say HERE it is.[/QUOTE]
How do I set this up to work on "my" number? Does it use worktodo.ini? William 
[QUOTE=wblipp]How do I set this up to work on "my" number? Does it use worktodo.ini?
William[/QUOTE] No it doesn't. When you run ./factor3_1 it asks for the exponent you want to run, the start and the stop bit. If you stop the program then restart it with the r parameter, and it will reload its status.txt file. [code] $ ./factor3_1 Please enter the exponent to be factored: 2^[I]3321928219[/I] Now enter start bit depth : [I]1[/I] Finally enter end bit depth : [I]67[/I] Sieving from 2^2 up to 2^67... [/code] HTH... Luigi 
[QUOTE=ET_]When you run ./factor3_1 it asks for the exponent you want to run[/QUOTE]
I tried "factor3_1 /?" and "factor3_1 3321928219" but I hadn't tried just plain "factor3_1". Thanks. William 
[QUOTE=wblipp]I tried "factor3_1 /?" and "factor3_1 3321928219" but I hadn't tried just plain "factor3_1". Thanks.
William[/QUOTE] My fault... I only tested r and h switches :redface: Glad it now works. :smile: Luigi 
I left factor3_1 running while I was away, and the computer was rebooted in my absence. I used the resume flag to restart the process, and it appears to be continuing from where it was shutdown. But can I be sure it didn't find any factors while I was away? Or do I need to repeat the search?

[QUOTE=wblipp]I left factor3_1 running while I was away, and the computer was rebooted in my absence. I used the resume flag to restart the process, and it appears to be continuing from where it was shutdown. But can I be sure it didn't find any factors while I was away? Or do I need to repeat the search?[/QUOTE]
You can be sure. :smile: Every time the program finds a factor, it writes a line on the screen AND on result.txt file. You only have to check out that file to be sure... :rolleyes: Happy hunting! Luigi 
Hi Luigi,
I compiled your factor3_1.c under Linux but I always get a segmentation fault when I try to start it. It asks for the exponent, the starting and ending bit, but then it stops with that segmentation fault. I haven't looked very much into the internals of your code. May be some of the GMParrays are too small or some pointers are computed wrong. Under some circumstances this could cause problems under Windows too... Has anyone else tested your program under Linux and/or other Unixlike operating systems?  Thomas 
[QUOTE=Thomas11]Hi Luigi,
I compiled your factor3_1.c under Linux but I always get a segmentation fault when I try to start it. It asks for the exponent, the starting and ending bit, but then it stops with that segmentation fault. I haven't looked very much into the internals of your code. May be some of the GMParrays are too small or some pointers are computed wrong. Under some circumstances this could cause problems under Windows too... Has anyone else tested your program under Linux and/or other Unixlike operating systems?  Thomas[/QUOTE] I did :))) Factor3_1.c has been successfully compiled under Linux Mandrake 9.2, with GMP 4.1.2 and a Xeon PIII @ 500 MHz. I noticed no malfunctioning at all. I myself ran across that "segmentation fault" problem. In my case was a matter of libraries' path. Anyway, I will recheck my source code and recompile to see what happened, then I will send here a (hopefully working) gzipped copy tomorrow as soon as I get to my office. Luigi 
GMP allocates space for the numbers on the stack, instead of the heap. If you make a number that's too large, you'll run out of stack space and get a segfault.
They do this for speed. If you want numbers to be allocated from the heap, you have to specify it when you compile the library. 
There are two things wrong with factor3_1.
1. It says it could not find cygwin1.dll and I need to reinstall the application. 2. I think it is in Italian. Perhaps me or someone could translate it to English. 
[QUOTE=clowns789]There are two things wrong with factor3_1.
1. It says it could not find cygwin1.dll and I need to reinstall the application. 2. I think it is in Italian. Perhaps me or someone could translate it to English.[/QUOTE] Do you have cygwin installled and on the path? I didn't, but it was pretty easy to Google cygwin and follow the instructions. The version of factor3_1 that I downloaded from the link is in English. William 
You don't need to install cygwin, just google for the two dll's the program asks for and put them in the same directory.

The second smallest Billion Digit candidate, 3321928219, has no factors through 67 bits. Continuing onward.
William 
[QUOTE=wblipp]The second smallest Billion Digit candidate, 3321928219, has no factors through 67 bits. Continuing onward.
William[/QUOTE] Congrats! :smile: Should you need any "factoring" help, just ask! :cool: Luigi 
[QUOTE=ET_]Should you need any "factoring" help, just ask![/QUOTE]
Well, [I]your[/I] number is the smallest candidate, M3321928171. As of the last update, you had trial factored it to 67 bits. If you're not careful, I'll get past you on my number. William 
[QUOTE=wblipp]Well, [I]your[/I] number is the smallest candidate, M3321928171. As of the last update, you had trial factored it to 67 bits. If you're not careful, I'll get past you on my number.
William[/QUOTE] Are you going to keep on factoring your number? Which bit depth? I'll follow you! :flex: Luigi 
[QUOTE=smh]You don't need to install cygwin, just google for the two dll's the program asks for and put them in the same directory.[/QUOTE]
Which two? I downloaded cygwin1.dll and put it in the factor3_1 folder. That's one, but what about the other one? 
[QUOTE=ET_]Are you going to keep on factoring your number? Which bit depth?[/QUOTE]
I think we should make a plan for how to spread further and deeper. I suggest that we pick a base level. Then for each additional number under search, we go one bit deeper. Finally we pick a shape of either flat top or slope top. For example, if we pick a base of 67 bits and flat top, we would attempt to progress from one candidate at 67 bits to two candidates at 68 bits to three candidates at 69 bits etc. If we pick a base of 66 bits and slope top, we would attempt to go from one candidate at 66 bits to two at (67 and 66 bits) to three at (68, 67, 66 bits), etc. I like the 67 base, flat top approach. That would mean that you and I are presently working to take Operation Billion Digits to 2 candidates at 68 bits. If somebody else joins us, we could then all work towards 3 candidates at 69 bits. If nobody joins us, we probably take both candidates to 70 bits then find two more to jointly work towards four candidates at 70 bits. If you prefer more active candidates, we could set the base at 60 bits, the place where you originally quit. That would mean we should reach a good stopping place (68 bits for me), and then search for more candiidates  a flat top would require nine candidates at 68 bits. William 
[QUOTE=clowns789]Which two? I downloaded cygwin1.dll and put it in the factor3_1 folder. That's one, but what about the other one?[/QUOTE]
For me it also asked for cyggmp3.dll If the program is running, the file is probably somewhere in your path so there's no need to download it. 
I'll try the cyggmp thing.
But my original plans were to find a digit that couldn't be factored out at a low level and stick to that one. However, if it's a different computer you could probably do something else. So basically wblipp's plan is a good idea. 
[QUOTE=wblipp]
I like the 67 base, flat top approach. That would mean that you and I are presently working to take Operation Billion Digits to 2 candidates at 68 bits. If somebody else joins us, we could then all work towards 3 candidates at 69 bits. If nobody joins us, we probably take both candidates to 70 bits then find two more to jointly work towards four candidates at 70 bits. [/QUOTE] I like your idea. It keeps work tightly connected and avoid wasting of time and resources. Let's go together towards 68 bits. :wink: [QUOTE=wblipp] If you prefer more active candidates, we could set the base at 60 bits, the place where you originally quit. That would mean we should reach a good stopping place (68 bits for me), and then search for more candiidates  a flat top would require nine candidates at 68 bits. William[/QUOTE] I'm not that skilled in managing distributed projects as you are... both ideas seem valuable, maybe the division line between them lies in the number of active participants: if you and I work alone, we may push the search towards any bit depth, while if other people join, they may prefer to stop early. :squash: Anyway, my exponent will be resubmitted as soon as my computer ends its P1 stage 2. Luigi 
[QUOTE=smh]For me it also asked for cyggmp3.dll
If the program is running, the file is probably somewhere in your path so there's no need to download it.[/QUOTE] I googled it up and couldn't find it. If you could post a link that would be great. 
[QUOTE=clowns789]I googled it up and couldn't find it. If you could post a link that would be great.[/QUOTE]
I couldn't find a link so I [URL=http://ElevenSmooth.com/Billion.html]made a link[/URL]. William 
I had some spare time on my Athlon XP 2100+, so...
M3321928171 no factor from 2^67 to 2^68. Luigi 
Better luck with 2^69?

[QUOTE=jinydu]Better luck with 2^69?[/QUOTE]
Sure! :bounce: In a couple of weeks... Luigi 
Isn't it possible to search for a factor to a depth other than 2^n? Because it seems that the amount of time needed to factor to the next depth would increase exponentially, making it impractical quite quickly.

[QUOTE=jinydu]Isn't it possible to search for a factor to a depth other than 2^n? Because it seems that the amount of time needed to factor to the next depth would increase exponentially, making it impractical quite quickly.[/QUOTE]
The time to trialfactor a number approximately doubles for each bit added. The search space itself grows more than 2 times: that's the reason why it is impractical trialfactoring a Mersenne number up to its bit length. OTOH the search for small bit depth is fast. LucasLehmer test doesn't look for factors. The original factoring program written by Andreas Pipp was based on k limits instead of 2^n limits: you could stop the search when d (the factor actually tried) reached a given size: I preferred to switch to 2^n to stay coherent with Prime95, although Factor3_1 prints k and d values as well. Luigi 
M3321928243 no factor from 2^2 to 2^60.
M3321928243 no factor from 2^2 to 2^60. M3321928307 no factor from 2^2 to 2^60. M3321928319 no factor from 2^2 to 2^60. M3321928373 no factor from 2^2 to 2^60. M3321928381 no factor from 2^2 to 2^60. M3321928391 has a factor: 260093705301737 M3321928391 has a factor: 578015540034001 M3321928417 no factor from 2^2 to 2^60. M3321928439 no factor from 2^2 to 2^60. :smile: NOW we can go on... Luigi P.S. I set up a mirror of Wblipp's Web page at [url]http://www.gimps.it/billion/billion.htm[/url] 
[QUOTE=ET_]I set up a mirror of Wblipp's Web page at
[url]http://www.gimps.it/billion/billion.htm[/url][/QUOTE] I've updated my [URL=http://ElevenSmooth.com/Billion.html]Billion Page[/URL] to include Luigi's latest results and to use his idea of preserving the finder of factors. Luigi  have you updated [url=http://www.garlic.com/~wedgingt/mersenne.html]Will Edgington[/url]? My number is presently at 67.892 digits. I've been hoping the originator of Operation Billion Digits, clowns789, will join us soon. William 
[QUOTE=wblipp]
Luigi  have you updated [url=http://www.garlic.com/~wedgingt/mersenne.html]Will Edgington[/url]? [/QUOTE] I did :smile: I'm exchanging emails with him since I started working on Mersenne factorizations, thank you! His new Facpriks.gz file will hopefully contain some new factors of ours :banana: Luigi 
[QUOTE=wblipp]My number is presently at 67.892 digits.[/QUOTE]
Ehhh, 2^67.892 i guess :wink: 
Just done a little bit of work, not planning to continue though.
[QUOTE]M3321928241 no factor from 2^60 to 2^61. M3321928243 no factor from 2^60 to 2^61. M3321928307 no factor from 2^60 to 2^61. M3321928319 no factor from 2^60 to 2^61. M3321928373 no factor from 2^60 to 2^61. M3321928381 no factor from 2^60 to 2^61. M3321928417 no factor from 2^60 to 2^61. M3321928439 no factor from 2^60 to 2^61.[/QUOTE] 
[QUOTE=smh]Just done a little bit of work, not planning to continue though.[/QUOTE]
Thanks smh :smile: 
[B]3321928219 has no factors through 2^68[/B]
That completes Level 2  Two billion digit candidates trial factored through 68 bits. A remarkable pall of reasonableness seems to have fallen over the community, with nobody jumping into this senseless project to claim the third candidate as thier own. Level 3 requires three candidates trial factored to 69 bits, so I'll stick with my number through that level and hope some knave joins our search by the time my Pentium Pro reaches 69 bits. [url]http://ElevenSmooth.com/Billion.html[/url] William 
[QUOTE=wblipp]
[url]http://ElevenSmooth.com/Billion.html[/url] William[/QUOTE] That link isn't working 
I'll reserve one of my computers for 3321928241 from 61 to 69

BTW, my friend had TFed all exponents that is up to 61 bit. You can raise the depth to 62 bit, no factors found

[QUOTE=HiddenWarrior]BTW, my friend had TFed all exponents that is up to 61 bit. You can raise the depth to 62 bit, no factors found[/QUOTE]
Taking the list to 63 bit... Carlo, a friend of mine, decided to join our whimsical search :) He got 3321928243, up to 70 bits. Luigi 
[QUOTE=jinydu]That link isn't working[/QUOTE]
Try [url]http://www.elevensmooth.com/Billion.html[/url] Luigi 
[QUOTE=ET_]Try [url]http://www.elevensmooth.com/Billion.html[/url][/QUOTE]
The link the cygwin1.dll wasn't working there. Also, I could not get it to run when I found a copy of cygwin1.dll on the net. 
[QUOTE=Uncwilly]The link the cygwin1.dll wasn't working there. Also, I could not get it to run when I found a copy of cygwin1.dll on the net.[/QUOTE]
There is another link here: [url]http://www.gimps.it/billion/billion.htm[/url] What system are you using? Luigi 
Well. I join the search and will try 3321928439.
MrHappy. :smile: 
Ok, that's functioning.

Holy cow! It looks like I spoke too soon about all the reasonable people.
I think I've got the [URL=http://home.earthlink.net/~elevensmooth/cygwin1.dll]cygwin1.dll link[/URL] working. I figure that Carlo has taken Operation Billion Digits to Level 2.2  three numbers to 68 digits then one to 69. It takes two more to 69 digits to reach Level 3 (3 numbers to 69 digits). I think I've captured all the advances at [url]http://ElevenSmooth.com/Billion.html[/url] As Buzz Lightyear would say, To Infinity and Beyond! William 
I will take one number to about 68bits maybe more. Here are the results so far:
M3321928307 no factor from 2^62 to 2^63. M3321928307 no factor from 2^63 to 2^65. I am running this on my Athalon 1100 (while P95 and the rest are going). If I run Linux, would I need the cygwin.dll's? Or won't that do it? I may try to refire my 200MMX into Linux. 
[QUOTE=Uncwilly]
I am running this on my Athalon 1100 (while P95 and the rest are going). If I run Linux, would I need the cygwin.dll's? Or won't that do it? I may try to refire my 200MMX into Linux.[/QUOTE] I never tried running the cygwin compiled version under Linux: in fact I recompiled Linux version from scratch after installing GMP libraries. But my Linux machine is out of reach until next week, and I cannot immediately put binaries online :sad: Luigi 
M3321928439 no factor to 2^68.

3321928319
is taken.

[QUOTE=nitro]is taken.[/QUOTE]
Welcome aboard, Nitro! The remaining exponents have been taken to 63 bit. Luigi :showoff: 
Optimizations
Factor3_1.exe has been compiled with Athlon optimizations, while my linux box is a Pentium III Xeon.
Source code is available for Pentium 4 optimizations under GMP, provided that the one who compiles the source sends me a working binary of the file. You should have a GMP library installed and made on a Pentium 4 machine to try this. Maybe we can squeeze a few more seconds out of this program. Luigi 
For me factor3_1 still isn't working. I got the two files, but it says the procedure entry point to cygwin1.dll isn't working.

[QUOTE=clowns789]For me factor3_1 still isn't working. I got the two files, but it says the procedure entry point to cygwin1.dll isn't working.[/QUOTE]
I assume that you have both libraries decompressed on the same directory where Factor3_1 is, on a Windows system. Which is your CPU? Luigi 
PII 363 MHZ

[QUOTE=clowns789]For me factor3_1 still isn't working. I got the two files, but it says the procedure entry point to cygwin1.dll isn't working.[/QUOTE]
I've changed from posting the dll's directly to posting a zip file of the two dlls. Try downloading them again and see if the problem goes away. [url]http://ElevenSmooth.com/Billion.html[/url] William 
Here are the results from my recent runs:
M3321928307 no factor from 2^65 to 2^68. M3321928319 no factor from 2^62 to 2^63. The second number I was only bumping it up (not taking it on as project). 
It would help if I checked the [B]current[/B] files... Oops, sorry, wasted cycles... :redface:

M3321928439 has a factor: 468552214000564196383 :showoff:
I'll try M3321928417. 
[QUOTE=MrHappy]M3321928439 has a factor: 468552214000564196383 :showoff:
I'll try M3321928417.[/QUOTE] Way to GO! It's the first factor we've found above the 60 bit level! For completness in the table at [url]http://ElevenSmooth.com/Billion.html[/url] , did you continue past this this factor to reach 2^69, or did you stop at the factor? Luigi  we ought to establish a standard operating procedure for who is going to inform Will Edgington about our discoveries. It males no difference to me  would you enjoy doing it or would rather have me take care of that detail? William 
[QUOTE=wblipp]For completness in the table at [url]http://ElevenSmooth.com/Billion.html[/url] , did you continue past this this factor to reach 2^69, or did you stop at the factor?[/QUOTE]
I stopped at the factor. Should i proceed to the next bit level the next time? 
[QUOTE=wblipp]
Luigi  we ought to establish a standard operating procedure for who is going to inform Will Edgington about our discoveries. It males no difference to me  would you enjoy doing it or would rather have me take care of that detail? William[/QUOTE] I will take care of this job... tomorrow. I already sent him about 14,000 factors above 79,3M :smile: Congrats, MrHappy! :bow: Luigi 
[QUOTE=MrHappy]I stopped at the factor.
Should i proceed to the next bit level the next time?[/QUOTE] I guess you should complete the range up to 69 bit to be sure no other factors hide in it, then (as Wblipp pointed out) move to the previous range (3321928417). Luigi 
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