User group for PFGW & PrimeForm programs Yahoo Group Invitation for 101 titanic helpers =============================================== Jens Kruse Andersen Message 1 of 19 Jan 7, 2005 ----------------------------------------------- The first 101 titanic primes are 10^999+n for the following n: 7, 663, 2121, 2593, 3561, 4717, 5863, 9459, 11239, 14397, 17289, 18919, 19411, 21667, 25561, 26739, 27759, 28047, 28437, 28989, 35031, 41037, 41409, 41451, 43047, 43269, 43383, 50407, 51043, 52507, 55587, 59877, 61971, 62919, 63177, 69229, 70777, 71893, 73203, 73209, 75301, 76447, 76969, 78463, 79923, 82243, 85837, 85971, 90079, 91737, 94281, 94699, 96081, 97807, 102133, 104461, 105219, 121503, 122163, 122833, 122901, 124381, 126691, 129303, 130513, 133767, 136803, 137821, 137997, 140769, 143751, 144771, 145689, 145879, 146293, 151303, 152781, 153943, 155887, 155911, 156589, 158199, 163959, 164719, 165783, 168333, 170889, 171741, 175203, 176311, 177019, 184069, 184623, 184993, 187021, 189829, 195333, 197629, 198379, 201009, 203959. Prp'ed by PrimeForm/GW and proved by Marcel Martin's Primo. The product (10^999+7)*...*(10^999+203959) has 1549 characters but can be written on the short form (10^999+203959)#/(10^999)#. It has 100900 digits. I invite primeform readers to perhaps mess with Chris' parser by finding a prime on the form p = k*420*(10^999+203959)#/(10^999)#-1, for k<10^9. I recall reading about the Primeform e-group (before my time) but the biography is currently specific for another 100k prime: http://primes.utm.edu/bios/page.php?id=339 I have sieved to 10^12 such that p+2, 2p+1 and (p-1)/2 are also unfactored. This gives a small bonus twin chance and two Sophie Germain chances, all provable. This is not the fastest method to search those records but it's a free chance. Mail me for a PrimeForm ABC file (with the long product) if you want to participate. Around 4700 prp tests are expected to find a prime. 101 titanic helpers in pfgw -tc must be some sort of record. Puzzle: How many titanic primality proofs are at least needed to prove primality for a number on the form k*(10^999+203959)#/(10^999)#-1? -- Jens Kruse Andersen =============================================== David Broadhurst Message 2 of 19 Jan 8, 2005 ----------------------------------------------- > Puzzle: How many titanic primality proofs are at least > needed to prove primality for a number on the form > k*(10^999+203959)#/(10^999)#-1? Answer: 101, else the formula cannot be reliably parsed. Note: having proven all 101, only 31 are needed for KP. Nice one, Jens. Please email me a sieved ABC file. David =============================================== Paul Underwood Message 3 of 19 Jan 8, 2005 ----------------------------------------------- Hi, > I recall reading about the Primeform e-group (before my time) but the > biography is currently specific for another 100k prime: > http://primes.utm.edu/bios/page.php?id=339 > I have the password for this Bio. I will update it with any blurb written by others relavent to e-group projects. Current projects: Jens' 100 titanic helper prime. Minimal provable 100k prime (on the back boiler somewhere). Gigantic CHG proven prime. > Mail me for a PrimeForm ABC file (with the long product) if you want to > participate. > Around 4700 prp tests are expected to find a prime. Count me in. Mail me some 500 numbers to be tested -- I should be able to complete these in less than a month at 1GHz. Paul =============================================== Pierre CAMI Message 4 of 19 Jan 8, 2005 ----------------------------------------------- --- In primeform@yahoogroups.com, "Jens Kruse Andersen" wrote: > The first 101 titanic primes are 10^999+n for the following n: > 7, 663, 2121, 2593, 3561, 4717, 5863, 9459, 11239, 14397, 17289, 18919, > 19411, 21667, 25561, 26739, 27759, 28047, 28437, 28989, 35031, 41037, 41409, > 41451, 43047, 43269, 43383, 50407, 51043, 52507, 55587, 59877, 61971, 62919, > 63177, 69229, 70777, 71893, 73203, 73209, 75301, 76447, 76969, 78463, 79923, > 82243, 85837, 85971, 90079, 91737, 94281, 94699, 96081, 97807, 102133, > 104461, 105219, 121503, 122163, 122833, 122901, 124381, 126691, 129303, > 130513, 133767, 136803, 137821, 137997, 140769, 143751, 144771, 145689, > 145879, 146293, 151303, 152781, 153943, 155887, 155911, 156589, 158199, > 163959, 164719, 165783, 168333, 170889, 171741, 175203, 176311, 177019, > 184069, 184623, 184993, 187021, 189829, 195333, 197629, 198379, 201009, > 203959. > > Prp'ed by PrimeForm/GW and proved by Marcel Martin's Primo. > > The product (10^999+7)*...*(10^999+203959) has 1549 characters but can be > written on the short form (10^999+203959)#/(10^999)#. It has 100900 digits. > > I invite primeform readers to perhaps mess with Chris' parser by finding a > prime on the form > p = k*420*(10^999+203959)#/(10^999)#-1, for k<10^9. > I recall reading about the Primeform e-group (before my time) but the > biography is currently specific for another 100k prime: > http://primes.utm.edu/bios/page.php?id=339 > > I have sieved to 10^12 such that p+2, 2p+1 and (p-1)/2 are also unfactored. > This gives a small bonus twin chance and two Sophie Germain chances, > all provable. > This is not the fastest method to search those records but it's a free chance. > > Mail me for a PrimeForm ABC file (with the long product) if you want to > participate. > Around 4700 prp tests are expected to find a prime. > > 101 titanic helpers in pfgw -tc must be some sort of record. > Puzzle: How many titanic primality proofs are at least needed to prove > primality for a number on the form k*(10^999+203959)#/(10^999)#-1? > > -- > Jens Kruse Andersen ******************** Count me in. Mail me some 500 numbers to be tested please Respectfull regards , Pierre =============================================== Jens Kruse Andersen Message 5 of 19 Jan 8, 2005 ----------------------------------------------- David Broadhurst wrote: > > Puzzle: How many titanic primality proofs are at least > > needed to prove primality for a number on the form > > k*(10^999+203959)#/(10^999)#-1? > > Answer: 101, else the formula cannot be reliably parsed. Yes, it was a trick question. I was careful to certify and validate all 101 before sieving and prp'ing, although a pseudoprime like this would be a far greater discovery than a 100k prime. > Note: having proven all 101, only 31 are needed for KP. Yes, and if anybody can get below 31, it will be David. Whoever finds the prp, I suggest using pfgw -tc in the original proof in order to use all 101. Paul Underwood wrote: > > http://primes.utm.edu/bios/page.php?id=339 > > I have the password for this Bio. I will update it with any blurb > written by others relavent to e-group projects. Great. It would be nice to find more e-group primes. I have so far mailed sieved files (and a helper file with 101 primes) to: David Broadhurst Predrag Minovic Paul Underwood Thanks to everybody. -- Jens Kruse Andersen =============================================== David Broadhurst Message 6 of 19 Jan 8, 2005 ----------------------------------------------- > Around 4700 prp tests are expected to find a prime. So the depth of the sieve was about 10^(exp(-Euler)*100900/4700) = 1.1T =============================================== jim_fougeron Message 7 of 19 Jan 8, 2005 ----------------------------------------------- --- In primeform@yahoogroups.com, "David Broadhurst" wrote: > > > Puzzle: How many titanic primality proofs are at least > > needed to prove primality for a number on the form > > k*(10^999+203959)#/(10^999)#-1? > > Answer: 101, else the formula cannot be reliably parsed. > > Note: having proven all 101, only 31 are needed for KP. > > Nice one, Jens. Please email me a sieved ABC file. > > David A note to participants. I would strongly NOT recommend using a -tc for a form such as this. There is no reason at all to use -tc for this, and it will cause the proof to take around 6x as long as a simple -t (which is what should be used) test. The -tc has had all "short out" optimizations removed. The -t (or -tp) will bail out with a proof, as soon as enough factor data has been accumualted. Even at the -t level, the above will be VERY slow, due to exponentation requiring 3 FFT's for the square-mod, and 6 FFT's for the square-mul-mod (due to generic reduction, and due to the exponentation "base" being a LARGE number). Also, the -tp is 1.5 to 2x slower, due to more complex square-mod and square-mul-mod logic required. Of course, a -tc "can" be used, but my question is why? Jim. =============================================== Ken Davis Message 8 of 19 Jan 8, 2005 ----------------------------------------------- Hi Jens, I'll take 500 also if that's OK Cheers Ken --- In primeform@yahoogroups.com, "Jens Kruse Andersen" wrote: > The first 101 titanic primes are 10^999+n for the following n: > 7, 663, 2121, 2593, 3561, 4717, 5863, 9459, 11239, 14397, 17289, 18919, > 19411, 21667, 25561, 26739, 27759, 28047, 28437, 28989, 35031, 41037, 41409, > 41451, 43047, 43269, 43383, 50407, 51043, 52507, 55587, 59877, 61971, 62919, > 63177, 69229, 70777, 71893, 73203, 73209, 75301, 76447, 76969, 78463, 79923, > 82243, 85837, 85971, 90079, 91737, 94281, 94699, 96081, 97807, 102133, > 104461, 105219, 121503, 122163, 122833, 122901, 124381, 126691, 129303, > 130513, 133767, 136803, 137821, 137997, 140769, 143751, 144771, 145689, > 145879, 146293, 151303, 152781, 153943, 155887, 155911, 156589, 158199, > 163959, 164719, 165783, 168333, 170889, 171741, 175203, 176311, 177019, > 184069, 184623, 184993, 187021, 189829, 195333, 197629, 198379, 201009, > 203959. > > Prp'ed by PrimeForm/GW and proved by Marcel Martin's Primo. > > The product (10^999+7)*...*(10^999+203959) has 1549 characters but can be > written on the short form (10^999+203959)#/(10^999)#. It has 100900 digits. > > I invite primeform readers to perhaps mess with Chris' parser by finding a > prime on the form > p = k*420*(10^999+203959)#/(10^999)#-1, for k<10^9. > I recall reading about the Primeform e-group (before my time) but the > biography is currently specific for another 100k prime: > http://primes.utm.edu/bios/page.php?id=339 > > I have sieved to 10^12 such that p+2, 2p+1 and (p-1)/2 are also unfactored. > This gives a small bonus twin chance and two Sophie Germain chances, > all provable. > This is not the fastest method to search those records but it's a free chance. > > Mail me for a PrimeForm ABC file (with the long product) if you want to > participate. > Around 4700 prp tests are expected to find a prime. > > 101 titanic helpers in pfgw -tc must be some sort of record. > Puzzle: How many titanic primality proofs are at least needed to prove > primality for a number on the form k*(10^999+203959)#/(10^999)#-1? > > -- > Jens Kruse Andersen =============================================== Paul Underwood Message 9 of 19 Jan 8, 2005 ----------------------------------------------- --- In primeform@yahoogroups.com, "jim_fougeron" wrote: > > --- In primeform@yahoogroups.com, "David Broadhurst" > wrote: > > > > > Puzzle: How many titanic primality proofs are at least > > > needed to prove primality for a number on the form > > > k*(10^999+203959)#/(10^999)#-1? > > > > Answer: 101, else the formula cannot be reliably parsed. > > > > Note: having proven all 101, only 31 are needed for KP. > > > > Nice one, Jens. Please email me a sieved ABC file. > > > > David > > A note to participants. I would strongly NOT recommend using a -tc > for a form such as this. There is no reason at all to use -tc for > this, and it will cause the proof to take around 6x as long as a > simple -t (which is what should be used) test. The -tc has had all > "short out" optimizations removed. The -t (or -tp) will bail out > with a proof, as soon as enough factor data has been accumualted. > Jim, shouldn't that be -tp with a helper file? -tp N+1 test. uses the N+1 test to check whether the number is prime. This is NOT a probable test. You will want to use this mode whenever your number is easily factorable when you add 1. (for example n!-1) If the factorisation is less then 33.33%, an F-strong test will be performed. Paul =============================================== jim_fougeron Message 10 of 19 Jan 8, 2005 ----------------------------------------------- --- In primeform@yahoogroups.com, "Paul Underwood" wrote: > > --- In primeform@yahoogroups.com, "jim_fougeron" wrote: > > > > There is no reason at all to use -tc for > > this, and it will cause the proof to take around 6x as long as a > > simple -t (which is what should be used) test. The -tc has had all > > shouldn't that be -tp with a helper file? > > -tp N+1 test. > You are correct. The -tp is what "should" be used. However, the -tp is much slower than the -t (-tm). If the original search would have used k*(huge semi-priorial)+1 then the faster -t would have been sufficient. As for people using the -tc when they really do not need to, I simply have to ask "why?" A proven prime is not any "more" proven by using -tc, vs using a different yet sufficient form, so I don't see the point in that, other than to burnin test your CPU, or to test the software. Jim. =============================================== David Broadhurst Message 11 of 19 Jan 8, 2005 ----------------------------------------------- Err, Jim, I hope you understood the point in http://groups.yahoo.com/group/primeform/message/5202 to which you appended your -tc comments in http://groups.yahoo.com/group/primeform/message/5207 My point was that one must [*] prove all the probable primes in the construct even though one does not have to use them all in the proof. My message in no way suggested using -tc. In fact I commented that a KP proof would use even _fewer_ primes than would be used by -tp. David (puzzled by your message linking) [*] else the primorial formula has an unknown result! =============================================== Jens Kruse Andersen Message 12 of 19 Jan 8, 2005 ----------------------------------------------- I have now mailed candidates to: David Broadhurst Predrag Minovic (twice) Paul Underwood Pierre Cami Ken Davis Phil Carmody Minovic reported not getting my first mail. Let me know if others are missing. Thanks for the great response. I didn't expect 6 people in 14 hours. Maybe it was clever to refer to the old Primeform e-group. Jim Fougeron wrote: > Of course, a -tc "can" be used, but my question is why? Seen the subject? It just seemed fun to use 100+ titanic helpers in a proof but I may have a strange idea of fun. Most people probably think anything about primes is a strange idea of fun. With 4700 prp tests expected, a slow proof is acceptable to me but -tc is optional for the lucky discoverer. If he mails me an unproven prp then I will gladly use cycles on -tc. By the way, I chose the form ...-1 over ...+1 because ...-1 gave two bonus Sophie Germain chances while ...+1 "only" gave two CC2 2nd kind chances (I know SG = CC2 1st kind). -- Jens Kruse Andersen =============================================== David Broadhurst Message 13 of 19 Jan 12, 2005 ----------------------------------------------- After 1205 tests, I found a PRP and am now running -tp. Watch this space... =============================================== Jens Kruse Andersen Message 14 of 19 Jan 12, 2005 ----------------------------------------------- David Broadhurst wrote: > After 1205 tests, I found a PRP and am now running -tp. > Watch this space... Wow. That was fast. That makes 12 tests per hour since candidates were mailed to David. Quite a few GHz at work it seems. It's only an hour since I mailed candidates to the 7th contributer Luigi Morelli who mailed today. I guess he should be credited for good will :-) -- Jens Kruse Andersen (watching) =============================================== David Broadhurst Message 15 of 19 Jan 12, 2005 ----------------------------------------------- > Wow. That was fast. My sysman was commissioning a cluster of xenons and I offered my services as unofficial frier. Only one xenon died in the attempt :-) David =============================================== Ken Davis Message 16 of 19 Jan 12, 2005 ----------------------------------------------- That is fast. I've only done 123 of my 500 (no prps yet). I'm still planning to complete the range (who knows we might get more than one) Cheers Ken --- In primeform@yahoogroups.com, "Jens Kruse Andersen" wrote: > David Broadhurst wrote: > > > After 1205 tests, I found a PRP and am now running -tp. > > Watch this space... > > Wow. That was fast. > That makes 12 tests per hour since candidates were mailed to David. > Quite a few GHz at work it seems. > It's only an hour since I mailed candidates to the 7th contributer > Luigi Morelli who mailed today. > I guess he should be credited for good will :-) > > -- > Jens Kruse Andersen (watching) =============================================== Paul Underwood Message 17 of 19 Jan 12, 2005 ----------------------------------------------- --- In primeform@yahoogroups.com, "Ken Davis" wrote: > > That is fast. It was! David must have O(20GHz) on the job. > I've only done 123 of my 500 (no prps yet). I have done 63 tests at 1GHz -- 100 minutes per test. > I'm still planning to complete the range (who knows we might get > more than one) I am also going to complete my range of 500 candidates. Congratualtions David. Paul ( waiting to see how Chris' submission parser copes ) > --- In primeform@yahoogroups.com, "Jens Kruse Andersen" > wrote: > > David Broadhurst wrote: > > > > > After 1205 tests, I found a PRP and am now running -tp. > > > Watch this space... > > > > Wow. That was fast. > > That makes 12 tests per hour since candidates were mailed to David. > > Quite a few GHz at work it seems. > > It's only an hour since I mailed candidates to the 7th contributer > > Luigi Morelli who mailed today. > > I guess he should be credited for good will :-) > > > > -- > > Jens Kruse Andersen (watching) =============================================== David Broadhurst Message 18 of 19 Jan 12, 2005 ----------------------------------------------- Paul: > waiting to see how Chris' submission parser copes Oh, I think that when/if the -tp job completes satisfactorily you really _should_ submit the primorial form, just to remind Chris that I am not really the helpful person that I have tried to be recently, but instead a total p-i-t-a, thanks to Jens :-) Of course, the primorial form would not get through the submission parser, which would not be able to compute the number of digits. But it could well cause a fair deal of trouble before the parser fails ... Then Chris can enter Jens' gloriously short form manually. Anyway, this is idle speculation, until -tp completes... David =============================================== gchil0 Message 19 of 19 Jan 12, 2005 ----------------------------------------------- Having now caught up on all the messages sent over the holidays, I was going to offer a bit of computing time...but never mind. Congrats David! Greg --- In primeform@yahoogroups.com, "David Broadhurst" wrote: > > After 1205 tests, I found a PRP and am now running -tp. > Watch this space... =============================================== Cached by Georg Fischer at Nov 14 2019 12:47 with clean_yahoo.pl V1.4