P.I.E.S. - Prime Internet Eisenstein Search

[Batalov]

Once upon a time, there was a wonderful "non-boring" prime search project, names P.I.E.S. and its logo was the best of them all!

I've inadvertently revived it recently (D.Broadhurst brought to my attention the Ecclesiastical truth that nothing is new under the sun).
Some of the recent primes include these:

Phi(3, -16159^78732)	662674 digits
Phi(3, -13617^41472)	342898 digits
Phi(3, -9499^41472) 	329925 digits
Phi(3, -14809^36864)	307485 digits
Phi(3, -1925^46656)	306477 digits
Phi(3, -12890^36864)	303041 digits
Phi(3, -29906^32768)	293324 digits
Phi(3, -25719^32768)	289031 digits

[rogue]

I remember that project. Whatever happened to Phil Carmody? That was his baby.

[Batalov]

His CV seems rather current (on his famous website).

Probably gave up primes to further his real work: Tizen, Linux, security...
...and bitter (!). The dude rated >9000 beers. That's awesome.
________________________

P.S. (much later) In November, I received an answer from Phil! He is alive and well, and to use his words, "I like to
think of it as taking a break, I'm sure I'll be back some time..." It is a rather long break from anything numerical.

[Batalov]

Yves Gallot independently got interested in this form.
At this time, he wrote a fast (for those who know, like a Genefer_OCL fast!) test implementation for Phi(3*2^n,b).
Version 0.1-beta, currently. It runs great!

Here is the thread where development news will be announced. (No need to cross-post here; it will be happening there.)

[axn]

Originally Posted by Batalov

Yves Gallot independently got interested in this form.
At this time, he wrote a fast (for those who know, like a Genefer_OCL fast!) test implementation for Phi(3*2^n,b).
Version 0.1-beta, currently. It runs great!

Here is the thread where development news will be announced. (No need to cross-post here; it will be happening there.)

In that thread, you mentioned that you had adapted mfaktc for sieving. Do you have any stats sieve depth/time for a single candidate?

[Batalov]

Optimal depth? I haven't checked systematically.

But in practice, for some ranges I prefactored to 55 bits, or even 59-61 bits (for E-M numbers).
I patched only one kernel, so the limit is 63 bits iirc.

For the form chosen by Yves, a modification to ppsieve/tpsieve is rather more appropriate (because 2^n is fixed) - to really sieve as opposed to prefactoring. I have not looked into tpsieve source.

EDIT: ...Or rather AthGFNSieve ?

EDIT 2: ...Or gfnsvCUDA, in fact?

[Batalov]

Here are some 1P-4.5P range factors -- for debugging the future CycSvCUDA+, attached.
(these are not all factors, because my prefactoring is not sieveless, and my range is definitely not up to 100M... I aim to run Cyclo only up to 60-100k, so I refactored only that and on CPU, because GPUs are all busy with Cyclo.)

[axn]

1000001261273089 | 662808^262144-662808^131072+1
1000006089965569 | 849574^262144-849574^131072+1
1000008375336961 | 455269^262144-455269^131072+1
1000015658483713 | 609424^262144-609424^131072+1
1000041403908097 | 920824^262144-920824^131072+1
1000111040888833 | 919807^262144-919807^131072+1
1000150692790273 | 604203^262144-604203^131072+1
1000162177843201 | 29180^262144-29180^131072+1
1000174155988993 | 787542^262144-787542^131072+1
1000316228861953 | 398024^262144-398024^131072+1
1000349961289729 | 531076^262144-531076^131072+1
1000367180218369 | 411263^262144-411263^131072+1
1000377009831937 | 159202^262144-159202^131072+1
1000382286790657 | 617552^262144-617552^131072+1
1000383456215041 | 875212^262144-875212^131072+1
1000386632613889 | 546295^262144-546295^131072+1
1000397529415681 | 795057^262144-795057^131072+1
1000399998812161 | 866961^262144-866961^131072+1
1000401672339457 | 390886^262144-390886^131072+1
1000405490466817 | 688428^262144-688428^131072+1
1000433433968641 | 615190^262144-615190^131072+1
1000448240910337 | 138781^262144-138781^131072+1
1000484790337537 | 900170^262144-900170^131072+1
1000522517053441 | 562276^262144-562276^131072+1
1000548104404993 | 679006^262144-679006^131072+1
1000582061752321 | 350276^262144-350276^131072+1
1000662300622849 | 660924^262144-660924^131072+1
1000663461396481 | 837503^262144-837503^131072+1
1000665327599617 | 68496^262144-68496^131072+1
1000689321639937 | 860734^262144-860734^131072+1
1000756578091009 | 436685^262144-436685^131072+1
1000782285766657 | 506314^262144-506314^131072+1
1000823339089921 | 312141^262144-312141^131072+1
1000831513264129 | 173543^262144-173543^131072+1
1000832908394497 | 119875^262144-119875^131072+1
1000865864613889 | 224861^262144-224861^131072+1
1000872873295873 | 704347^262144-704347^131072+1
1000890549927937 | 558663^262144-558663^131072+1
1000963792699393 | 839906^262144-839906^131072+1
1001002085646337 | 783593^262144-783593^131072+1
1001055949946881 | 894642^262144-894642^131072+1
1001056090718209 | 944650^262144-944650^131072+1
1001170787106817 | 663236^262144-663236^131072+1
1001192796192769 | 197537^262144-197537^131072+1
1001399841718273 | 564133^262144-564133^131072+1
1001406565711873 | 849776^262144-849776^131072+1
1001418572169217 | 44447^262144-44447^131072+1
1001456317759489 | 764595^262144-764595^131072+1
1001518338932737 | 299751^262144-299751^131072+1
1001569924939777 | 478068^262144-478068^131072+1
1001593326010369 | 261012^262144-261012^131072+1
1001616896950273 | 801407^262144-801407^131072+1
1001676709036033 | 812043^262144-812043^131072+1
1001678214266881 | 128706^262144-128706^131072+1
1001705339092993 | 518811^262144-518811^131072+1
1001713621794817 | 675413^262144-675413^131072+1
1001721493979137 | 255905^262144-255905^131072+1
1001770557112321 | 559012^262144-559012^131072+1
1001789048487937 | 495255^262144-495255^131072+1
1001861382144001 | 82525^262144-82525^131072+1
1001868515868673 | 984503^262144-984503^131072+1
1001907340443649 | 274058^262144-274058^131072+1
1001959949598721 | 642412^262144-642412^131072+1
1001964683919361 | 154312^262144-154312^131072+1
1002008130355201 | 365738^262144-365738^131072+1
1002024444100609 | 759309^262144-759309^131072+1
1002039045783553 | 976621^262144-976621^131072+1
1002062479884289 | 571005^262144-571005^131072+1
1002063413379073 | 164798^262144-164798^131072+1
1002067929071617 | 637688^262144-637688^131072+1
1002081327513601 | 715174^262144-715174^131072+1
1002082203598849 | 553527^262144-553527^131072+1
1002138634813441 | 168077^262144-168077^131072+1
1002141614604289 | 781507^262144-781507^131072+1
1002174755635201 | 403241^262144-403241^131072+1
1002234780057601 | 775690^262144-775690^131072+1
1002236961619969 | 35954^262144-35954^131072+1
1002282297065473 | 218326^262144-218326^131072+1
1002318097809409 | 963807^262144-963807^131072+1
1002318530347009 | 222129^262144-222129^131072+1
1002355201671169 | 116983^262144-116983^131072+1
1002363982970881 | 910301^262144-910301^131072+1
1002380442992641 | 265570^262144-265570^131072+1
1002405397266433 | 857181^262144-857181^131072+1
1002443680776193 | 391413^262144-391413^131072+1
1002455260987393 | 408596^262144-408596^131072+1
1002469296439297 | 572274^262144-572274^131072+1
1002621944463361 | 649746^262144-649746^131072+1
1002623702138881 | 803789^262144-803789^131072+1
1002701292306433 | 599480^262144-599480^131072+1
1002767977021441 | 613955^262144-613955^131072+1
1002785934409729 | 484050^262144-484050^131072+1
1002801935155201 | 609590^262144-609590^131072+1
1002813331341313 | 237504^262144-237504^131072+1
1002906852261889 | 232118^262144-232118^131072+1
1002932443545601 | 667371^262144-667371^131072+1
1002933212676097 | 42134^262144-42134^131072+1
1002946889515009 | 210015^262144-210015^131072+1
1002957273563137 | 709731^262144-709731^131072+1
1002977974812673 | 411432^262144-411432^131072+1
1003010488270849 | 517560^262144-517560^131072+1
1003098958725121 | 292353^262144-292353^131072+1
1003119180251137 | 806150^262144-806150^131072+1
1003140936892417 | 67015^262144-67015^131072+1
1003188995751937 | 977256^262144-977256^131072+1
1003210635214849 | 696010^262144-696010^131072+1
1003217749278721 | 537885^262144-537885^131072+1
1003222361702401 | 999668^262144-999668^131072+1
1003282991677441 | 618808^262144-618808^131072+1
1003308586893313 | 596060^262144-596060^131072+1
1003339550294017 | 468605^262144-468605^131072+1
1003356837642241 | 164382^262144-164382^131072+1
1003393092157441 | 843541^262144-843541^131072+1
1003393776353281 | 609351^262144-609351^131072+1
1003401657188353 | 315451^262144-315451^131072+1
1003417320554497 | 372292^262144-372292^131072+1
1003526908280833 | 827323^262144-827323^131072+1
1003556045586433 | 480595^262144-480595^131072+1
1003583148392449 | 452113^262144-452113^131072+1
1003583805849601 | 308705^262144-308705^131072+1
1003589516132353 | 892284^262144-892284^131072+1
1003635151208449 | 970300^262144-970300^131072+1
1003679915704321 | 30921^262144-30921^131072+1
1003727271493633 | 286751^262144-286751^131072+1
1003781934809089 | 627902^262144-627902^131072+1
1003850044538881 | 935433^262144-935433^131072+1
1003907933798401 | 680022^262144-680022^131072+1
1003908128833537 | 647373^262144-647373^131072+1
1003923660865537 | 638575^262144-638575^131072+1
1004079219474433 | 290709^262144-290709^131072+1
1004149336178689 | 484503^262144-484503^131072+1
1004241316478977 | 997454^262144-997454^131072+1
1004256750993409 | 83491^262144-83491^131072+1
1004297654894593 | 826337^262144-826337^131072+1
1004315414102017 | 600448^262144-600448^131072+1
1004371356942337 | 75431^262144-75431^131072+1
1004378840629249 | 959367^262144-959367^131072+1
1004493766656001 | 242570^262144-242570^131072+1
1004516072226817 | 168416^262144-168416^131072+1
1004528376741889 | 176092^262144-176092^131072+1
1004537894141953 | 899486^262144-899486^131072+1
1004576235061249 | 753402^262144-753402^131072+1
1004588756631553 | 708182^262144-708182^131072+1
1004760806719489 | 742124^262144-742124^131072+1
1004785497538561 | 417941^262144-417941^131072+1
1004806959267841 | 311457^262144-311457^131072+1
1004848089661441 | 249561^262144-249561^131072+1
1004902519406593 928.8/s (2.2P/day) Found 147 ETA 10h57m
Termination requested

First output from the sieve (b <= 1e6)

[Batalov]

Looks legit ;-)

[axn]

I will post a win32 binary later (once I've completed some more testing). It should complete a range 50% faster than GFN sieve (on account of the factor form k.3.2^n+1 as opposed to k.2^(n+1)+1)

Serge, would you be able to test it on Windows?

[rogue]

If you run these thru pfgw 3.7.8, it will validate them. Run you file as "pfgw factors.txt" and if all lines return "is Zero", then they are valid factors.