[ January 2013 ]Breaking news ! The search team made a hit !! ( Peter Kaiser, Kenneth Pedersen, Patrick De Geest ) The smallest MegaPRP has been found 10 ^{999999} + 593499and doublechecking as well as Primebase ( This pdf file is very huge [44 MB] so be patient till it's fully downloaded.) |

The Minimum MegaPRP.
Firstpass and secondpass testers:
Software contributors:
Tutors:
The complete dataset wich contains data for all y values, ranging from y=1 to y=593499,
The PRP was found on December 24th 2012, by Peter Kaiser and was verified by
On January 15th 2013 our MegaPRP was verified as Strong-Fermat, Lucas and
On January 19th 2013 our MegaPRP was verified as Strong-Fermat, Lucas and
And finally on January 21st 2013 our MegaPRP was verified as Strong-Fermat,
This gives a total of 8 different prime-bases that each came back as PRP.
The project manager of "The Minimum MegaPRP search" wishes to thank all who helped
Go to the www.worldofnumbers.com website to get a full extraction of the dataset. |

This is a project started by Kenneth Egtved Pedersen. To become a success many helping hands were needed.

On a Q6600 2.4 GHz it takes an 8-24 hours to do just a single test, dependant on the value of y.

~~Will you join in ? Patience and a stroke of luck will link your name for ever to this discovery...~~

However we are not going to go too far with such an effort, if other people or projects have already conducted several years of search.

So, if you are aware of any individuals or projects searching for the first PRP megaprime please let us know.

From the Mersenne Forum... a discussion dd. 2006 !

in order to ensure that a PRP will actually be found. Kenneth is considering to sieve to p=10G.

Here is an open question :

Kenneth wrote [ *November 6, 2011* ] ¬

" I had 136237 candidates remaining at p=1G, and I expect to find around 21000 factors from p=1G to p=10G,

but I'll not know before next weekend for sure, how many factors were in the range. After having sieved to p=10G, I'll

hopefully be able to make a combined sievefile and sieve all remaining candidates on each core and then do 4 different

sieveranges at a time. I should even with a combined sievefile, be able to sieve ~2.1G each day."

Kenneth wrote [ *December 2, 2011* ] ¬

" I noticed that you have searched 10^999999+1011, that candidate I've a factor for, so it is a verified composite.

Thanks to Axn and Ken, I've now found out that using NewPGen is possible. When using the "AP: b^n+2k-1" function

in NewPGen, it is sieving approximately 10T a day on a Q6600 2.4 GHz. This is something like 10,000 times

faster than using srsieve. Currently the minimum sievedepth of the sievefile is 106T, with 87,563 candidates remaining.

Currently no one has joined the effort and maybe it isn't nescessary after all, since things are now progressing

beyond my wildest imaginations. Optimal sievedepth is currently around 2,000T, wich will be reached nothing later

than by December 2012. I'm currently sieving from 106T-506T, and expect to get there by the end of this year.

Thanks for hosting the details regarding my search. With a strike of luck and with my currently planned investment

in new CPU ressources, we may before the end of 2020 see the first possible MegaPRP. I'll give you the next update

as I get to p=1,000 T, wich will be late january or early february 2012."

Kenneth wrote [ *January 2, 2012* ] ¬

" Hi Patrick

Status: 83904 candidates remaining at 436.2T "

Kenneth wrote [ *January 13, 2012* ] ¬

" Status: 83745 candidates remaining at 463.5T

Ps. I'll do some testings on my Sandy bridge and see if I should stop sieving at p=1000T.

Most likely I'll reach optimal sievedepth at p=1000T, since the removal rate is getting close to 5 hours there.

So maybe before testing time gets to 5 hours we'll have a PRP for the project. "

Kenneth is nearing the end of sieving [ *February 24, 2012* ] ¬

" Tuesday 28 february the sieving of the Mega prp is reaching p=1000T, after that I'll put

some of my cores on the megasearch.

and there is ~82023 y's overall remaining in the sieve file :) "

Kenneth annouces [ *March 5, 2012* ] ¬

" I can inform you that p=1000T has been reached, there is ~83K untested candidates

remaining in sievefile. I'll continue sieving to p=2000T, since stopping now, is only abour 30%

of optimal sievedepth. So this means that for the next 100 days I'll only support your testing

by removing further factors from your test-ranges. I'll give you the exact number of untested

candidates remaining...

ps. New sieving range will take approximately 100 (IRL) days to complete, by then (I hope) a live

version of LLR supporting AVX will be released to the science community :) Anyways, AVX or not,

in 100 days I'll have all my current CRUS reservations completed and will be able to focus my resources 100%

on the MegaPRP search :) Hope you can manage another 100 days on your self (Maybe less if I sieve

using my Sandy Bridge, wich is possible in less than 100 days, to be able to do).

ps2. 'CRUS' is short for Conjectures 'R' US, wich is a subproject under the PrimeProjects list at

the mersenneforum, where those who support the project, tries to prove as many conjectures on the

sierpinski aswell on the Riesel side for bases <=1030, as possible. If you're familiar with the former

RieselSieve project, then what CRUS does is the same as what RieselSieve did for RieselBase2conjecture only,

while CRUS tries to do it for 1030 bases on both the riesel aswell the sierpinski side. So to sum up,

CRUS is about conjectures and about proving as many of them that can be proven in one lifetime,

as possible and to have all k's tested to n<=25000 for all the conjectures that can't be proven

in a lifetime for all bases <=1030."

Kenneth makes progress [ *March 18, 2012* ] ¬

" Hello Patrick

I have now sieved 200T more on our MegaPRP search, therby removing 325+ candidates..."

Kenneth informs [ *April 29, 2012* ] ¬

" Hello Patrick

I'm currently 45 days from reaching p=2000T as sievedepth. At that level it is about 490 minutes/factor.

My sandy bridge appears, when using Prime95 to take about 5.017 hours per test. So here is my current approach:

I've loaded the candidates from y=58231 to y<1M, a total of 15,251 tests at current sievedepth,

into a worktodo.txt file and started processing it with Prime95 version 27.6! My sandybridge is able to do

about 18 tests/day. I'll most likely continue sieving on my old Q6600 because it appears that optimal

sievedepth is around p=10,000T - so there is plenty of work to do. Never the less, it always helps save off

some doublechecks as sieving progresses towards further Peta's."

__Here is a discussion about older versions of Primeform and LLR and how they compare to each other.__

Kenneth wrote

If you decide to do PRP testing, please upgrade to LLR 3.8.5 or the most recent version of PFGW

since they have some flaw corrections and error checking wich makes their testresults more reliable

than previous versions wich used a bug filled GWNUM FFT library :)

A slightly worried Patrick replied

In the past I did an upgrade of PFGW and found out that testing was considerably slower.

So I decided to stay with the then current version (I used the DOS running version 1.2.0 ...)

In that regard is LLR testing faster than PFGW ?

ps. the bug you mentioned in the 'GWNUM FFT library' how does it show up when using

old PFGW versions? I take it that when PFGW says a candidate is composite, it really is composite !

For many years I send PRP's to Lifchitz's TOP10000 list. Should I be worried now ?

A reassuring Kenneth answered

The bug affected PFGW versions is versions released around september 2010, all of them is between 3.3.0 and 3.3.5,

all bugs were fixed in version 3.3.6, so if you're using versions previous to the upgraded FFT library version (version 3.3.0 to 3.3.5)

then you are safe and sound. However if you want to have the same speed as LLR 3.8.5 (the most modern and bug free version of LLR)

and still want to use PFGW you should upgrade to at least pfgw 3.3.6 or newer versions .But you shouldn't be worried about your previous PRPs since they seem to have been found with the older and dreadfully slower GWNum library,

because before the new and upgraded FFT libraries, PFGW were considerably slower than newer versions of PFGW and of preupgraded versions of LLR.

However the non-upgraded versions of LLR and PFGW were known to have been thoroughly and extensively tested for bugs and none were found.

The only time that PFGW and LLR couldn't be used to compare their residues, was if one had a faulty CPU or RAM or HDD. So the morale of the story

is that your previous results should be good and flawless, so your PRPs send to the PRP list should be in fact PRPs. However a doublecheck with

PFGW version 3.3.6 or newer, using the -a1 (wich slows things down a bit but however uses a bigger FFT length wich is less prone to error) to see

what comes back. If your PRPs come back as composites then those are composites, however if your PRPs come back as PRPs then they are most certainly PRPs.

In regards to speed, there is no difference between the most recent version of LLR and the most recent version of PFGW. The bug if there is one,

either reveals it self as missed PRPs or primes or most often it shows up as a non-matching residue, wich means that a third testing is necessary

to show wich computer is right and wich is wrong.

ps. As mentioned above the

most recentversion of PFGW can be found at http://sourceforge.net/projects/openpfgw/files/ and this version is 3.3.7 .

I haven't used pfgw 3.3.7 , there may be some small speed-increases compared to 3.3.6 but as far as I know, the functions should overall still be the same.

__OpenPFGW and LLR formats for input files__

The PFGW file has no header since each line contains the number being worked on, such as: 10^999999+y,

while the LLR input file, contains a header and for each line it contains "y 999999", wich transforms into: 10^999999+y,

as a result of the information executed by the header of the file.

Here is the list of numbers that bite the dust !

Participants :

Kenneth Pedersen Peter Kaiser (a.k.a. PuzzlePeter) Patrick De Geest ( using PFGW Version 3.5.7.64BIT.20111115.Win_Stable [GWNUM 26.6] )

- 10^999999+500023 is composite: RES64: [654FBB930D3144F6]
- 10^999999+500071 is composite: RES64: [406B4D76A7EC7F5B]
- 10^999999+500073 is composite: RES64: [2F5515C1F61028F3]
- 10^999999+500079 is composite: RES64: [1276449F13E4E2F2]
- 10^999999+500181 is composite: RES64: [1F10C890931660CD]
- 10^999999+500229 is composite: RES64: [DDBF2F2DA868212B]
- 10^999999+500257 is composite: RES64: [78F122A2543CAC37]
- 10^999999+500329 is composite: RES64: [CEC65DFE98E95856]
- 10^999999+500493 is composite: RES64: [7EC43057103DCFA8]
- 10^999999+500521 is composite: RES64: [1B004E6AD6BF1FD0]
- 10^999999+500617 is composite: RES64: [2B925F3E61CA40F5]
- 10^999999+500671 is composite: RES64: [FC3CB7D3D93551AC]
- 10^999999+500673 is composite: RES64: [B0027DB722935D4C]
- 10^999999+500769 is composite: RES64: [CD529501DB0CA223]
- 10^999999+500773 is composite: RES64: [DAE092878E97161B]
- 10^999999+500833 is composite: RES64: [8B334D2FE9A75D97]
- 10^999999+501087 is composite: RES64: [CA27778C8A983DFC]
- 10^999999+501291 is composite: RES64: [BF33BAC80721778C]
- 10^999999+501321 is composite: RES64: [6D01DAFC3132E48C]
- 10^999999+501331 is composite: RES64: [086D1FB2E4959A20]
- 10^999999+501363 is composite: RES64: [69BFE19F71B2FAC7]
- 10^999999+501883 is composite: RES64: [EF20A2A80D7FD96B]
- 10^999999+501903 is composite: RES64: [A7EFD45F9EAE1599]
- 10^999999+501961 is composite: RES64: [D359415EED505925]
- 10^999999+502017 is composite: RES64: [270E1A53B099AFCA]
- 10^999999+502179 is composite: RES64: [D65033F18DC04D96]
- 10^999999+502341 is composite: RES64: [30664A6081E73D2D]
- 10^999999+502359 is composite: RES64: [1E29812FA947C98A]
- 10^999999+502467 is composite: RES64: [6B85B18A7D4B4F82]
- 10^999999+502519 is composite: RES64: [04D550AC013A8FDA]
- 10^999999+502521 is composite: RES64: [C4D10D11F3498137]
- 10^999999+502609 is composite: RES64: [16ADC9C5D45F49CB]
- 10^999999+502731 is composite: RES64: [7335DF29652C4A61]
- 10^999999+502747 is composite: RES64: [E3C1684A451F6F1A]
- 10^999999+502879 is composite: RES64: [81BD49430CD0780B]
- 10^999999+502953 is composite: RES64: [C38BA91BC1FEB032]
- 10^999999+503107 is composite: RES64: [AC7F65968A72600B]
- 10^999999+503109 is composite: RES64: [40DD88A1F70FA3A2]
- 10^999999+503113 is composite: RES64: [0A8D29392C06F396]
- 10^999999+503209 is composite: RES64: [CE08E7B0B2D7E20C]
- 10^999999+503211 is composite: RES64: [05725326F742D226]
- 10^999999+503353 is composite: RES64: [456DE02E974780B8]
- 10^999999+503389 is composite: RES64: [F7BD6ACC701BCE3C]
- 10^999999+503407 is composite: RES64: [09934725EB31DAE3]
- 10^999999+503431 is composite: RES64: [D04656EDC3D535D3]
- 10^999999+503487 is composite: RES64: [3069F44108ABD836]
- 10^999999+503533 is composite: RES64: [4FFA2B82DECFFD7C]
- 10^999999+503799 is composite: RES64: [4DD88097301B5884]
- 10^999999+503901 is composite: RES64: [AB633410635D6519]
- 10^999999+503929 is composite: RES64: [431E4BF26B7A88E1]
- 10^999999+503967 is composite: RES64: [9BCFD6DA26209B34]
- 10^999999+504007 is composite: RES64: [F463BF5856152011]
- 10^999999+504121 is composite: RES64: [F8A74EE3AD5FD127]
- 10^999999+504151 is composite: RES64: [1DAB171FF1853F46]
- 10^999999+504273 is composite: RES64: [1C255FF83AF4AE79]
- 10^999999+504433 is composite: RES64: [9555CDAD7FCA8CE2]
- 10^999999+504523 is composite: RES64: [21766EB11C426E63]
- 10^999999+504537 is composite: RES64: [A2199ADC31DD26E0]
- 10^999999+504579 is composite: RES64: [B53D7E8742E6A607]
- 10^999999+504697 is composite: RES64: [BC0F0CF979E74F64]
- 10^999999+504721 is composite: RES64: [2B70D91D9D421EED]
- 10^999999+504859 is composite: RES64: [15DD38F151040B3C]
- 10^999999+504861 is composite: RES64: [8B5CBCBA1704FF1A]
- 10^999999+504903 is composite: RES64: [4294A0D986C44B27]
- 10^999999+504963 is composite: RES64: [B136C4B644C9B7AE]
- 10^999999+717717 is composite: RES64: [60A9978CC3D817D1]
- 10^999999+723327 is composite: RES64: [47CF5F465769E995]
- 10^999999+735097 is composite: RES64: [908C4D5A51C28358]
- 10^999999+735139 is composite: RES64: [336F3E2F67BDB0DD]
- 10^999999+735297 is composite: RES64: [21C6373FCD851D62]
- 10^999999+735343 is composite: RES64: [D8F5F039F8D23CBD]
- 10^999999+735361 is composite: RES64: [1DC851E34ECC1479]
- 10^999999+735369 is composite: RES64: [03483784EC321B6A]
- 10^999999+735433 is composite: RES64: [7870F2595ED13C48]
- 10^999999+735447 is composite: RES64: [3D2BAD532E404D2B]
- 10^999999+735517 is composite: RES64: [09C04588B069759A]
- 10^999999+735579 is composite: RES64: [49FB6BC60C257188]
- 10^999999+735601 is composite: RES64: [F9D7C93325DA0A05]
- 10^999999+735711 is composite: RES64: [09D9AE939C57EF71]
- 10^999999+735721 is composite: RES64: [DAE3CE20E4B050F6]
- 10^999999+735733 is composite: RES64: [4052E71D7502857E]
- 10^999999+735787 is composite: RES64: [50A24D30106A5D58]
- 10^999999+735859 is composite: RES64: [4C65A7359C9DADD9]
- 10^999999+735877 is composite: RES64: [A9A63CE42A0963AD]
- 10^999999+735933 is composite: RES64: [F1B3730975ED3187]
- 10^999999+736039 is composite: RES64: [100752236F0609D3]
- 10^999999+736041 is composite: RES64: [AE90CB818B6F72FC]
- 10^999999+736201 is composite: RES64: [8C68675A5DA8DB06]
- 10^999999+736291 is composite: RES64: [5E2A844DC404D941]
- 10^999999+736339 is composite: RES64: [5CA76C5545DE9E57]
- 10^999999+736489 is composite: RES64: [44E01B99728986EB]
- 10^999999+736563 is composite: RES64: [E80DF733CEBBEE06]
- 10^999999+736719 is composite: RES64: [B7761C60F2DBDB4F]
- 10^999999+736903 is composite: RES64: [C5EA261C88DB5D69]
- 10^999999+740011 is composite: RES64: [08F292EE0C9DC757]
- 10^999999+740137 is composite: RES64: [83D8A7EA1278C988]
- 10^999999+740199 is composite: RES64: [2778449474E4FE88]
- 10^999999+740329 is composite: RES64: [AC7338C18F3F3FC7]
- 10^999999+740331 is composite: RES64: [E1CB249E295A06A9]
- 10^999999+740451 is composite: RES64: [817A1EF15F952569]
- 10^999999+740551 is composite: RES64: [B06B0A110652DF38]
- 10^999999+740673 is composite: RES64: [E7CA1805E31BA7EF]
- 10^999999+740707 is composite: RES64: [5D5F6C60CB245428]
- 10^999999+740743 is composite: RES64: [DCD1CAB71A5AFBBE]
- 10^999999+740799 is composite: RES64: [7ED5778895B04EDB]
- 10^999999+740907 is composite: RES64: [ED7DADD639FBB98A]
- 10^999999+740973 is composite: RES64: [46436B1C5F26F4EA]
- 10^999999+741099 is composite: RES64: [21FA89B964E3F833]
- 10^999999+741241 is composite: RES64: [0BEB6A1B81C29452]
- 10^999999+741283 is composite: RES64: [BC4DB11F87F91891]
- 10^999999+741373 is composite: RES64: [24AC705836122FA9]
- 10^999999+741387 is composite: RES64: [404F70AD84AFA5DF]
- 10^999999+741403 is composite: RES64: [D094BA5157A6C3BE]
- 10^999999+741433 is composite: RES64: [9838CD5EE240D046]
- 10^999999+741459 is composite: RES64: [15770BBECE9F2915]
- 10^999999+741507 is composite: RES64: [25D9EAD70C1BFA68]
- 10^999999+741523 is composite: RES64: [50E78DAD7ECEAE91]
- 10^999999+741813 is composite: RES64: [2AEF371CAFCAE227]
- 10^999999+741883 is composite: RES64: [933EC53B41DD2836]
- 10^999999+741961 is composite: RES64: [4937026BB48632F6]
- 10^999999+741991 is composite: RES64: [A3048538AC182603]
- 10^999999+792297 is composite: RES64: [0CEB1F144B679094]
- 10^999999+900001 is composite: RES64: [6C9BC931E8904A21]
- 10^999999+900063 is composite: RES64: [E98ECEB360208CA1]
- 10^999999+900067 is composite: RES64: [381994415A587C16]
- 10^999999+900139 is composite: RES64: [DF9C601CCB092C26]
- 10^999999+900163 is composite: RES64: [4DDA331A85FE2614]
- 10^999999+900231 is composite: RES64: [4BD1AE43E8B2DDC0]
- 10^999999+900331 is composite: RES64: [4D6F7C1C57094C4B]
- 10^999999+900429 is composite: RES64: [0B36A9EA13E5E11E]
- 10^999999+900517 is composite: RES64: [2990400B2EA50AAE]
- 10^999999+900717 is composite: RES64: [03F1F0AF24A45796]
- 10^999999+900741 is composite: RES64: [E20CD672D94AC534]
- 10^999999+900799 is composite: RES64: [CA746D084C12DDFE]
- 10^999999+900847 is composite: RES64: [5351E5FD21266CEF]
- 10^999999+900877 is composite: RES64: [F33CFB64E571F630]
- 10^999999+900907 is composite: RES64: [79641AB060588AE3]
- 10^999999+900991 is composite: RES64: [E788B5637330D776]
- 10^999999+901063 is composite: RES64: [D55699E8DA72866A]
- 10^999999+901117 is composite: RES64: [D7B88CCF3FF66749]
- 10^999999+901287 is composite: RES64: [974B3B60C4138075]
- 10^999999+901299 is composite: RES64: [56D320AD9602C497]
- 10^999999+901411 is composite: RES64: [9546F12F52721DFC]
- 10^999999+901441 is composite: RES64: [5DA6748A32EBAA43]
- 10^999999+901569 is composite: RES64: [E551C1678A2B4CDC]
- 10^999999+901659 is composite: RES64: [AB3744519897C469]
- 10^999999+901683 is composite: RES64: [59368C349F78C65F]
- 10^999999+901791 is composite: RES64: [BCCC38CDC7167AF5]
- 10^999999+901807 is composite: RES64: [28363E15DCE2458D]
- 10^999999+901849 is composite: RES64: [EBC793713C34BE64]
- 10^999999+901857 is composite: RES64: [20026D1216A89F06]
- 10^999999+901917 is composite: RES64: [9EE70E2C06BF7AAA]
- 10^999999+902011 is composite: RES64: [64811A9549B148D3]
- 10^999999+902073 is composite: RES64: [DDC1B54947998FCD]
- 10^999999+902143 is composite: RES64: [8764A6178AAD2930]
- 10^999999+902163 is composite: RES64: [7006EADBDD115B42]
- 10^999999+902247 is composite: RES64: [0CE551321FF76D5D]
- 10^999999+902277 is composite: RES64: [DB076A6138F8479D]
- 10^999999+902341 is composite: RES64: [5220728DA7AD2B81]
- 10^999999+902481 is composite: RES64: [37877998C0DEEDE5]
- 10^999999+902493 is composite: RES64: [35ADBA66BB46D22A]
- 10^999999+902499 is composite: RES64: [E87DE8D9F23912F9]
- 10^999999+902593 is composite: RES64: [C908229B7293E0D1]
- 10^999999+902601 is composite: RES64: [BBE3F465156562F8]
- 10^999999+903067 is composite: RES64: [A913A8ABDF4081E6]
- 10^999999+903087 is composite: RES64: [4202F54269FEC0F1]
- 10^999999+903139 is composite: RES64: [C598FB0B57B9E88F]
- 10^999999+903157 is composite: RES64: [A5A243E360A6F710]
- 10^999999+903219 is composite: RES64: [AB7AAB2CB58C5ACF]
- 10^999999+903511 is composite: RES64: [CCEBE416D71E9EE4]
- 10^999999+903567 is composite: RES64: [440BEB9F26A61858]
- 10^999999+903639 is composite: RES64: [93B0D8814179919A]
- 10^999999+903903 is composite: RES64: [E40D6A39FA8AD4BB]
- 10^999999+903973 is composite: RES64: [385E9FC73B7EDA5A]
- 10^999999+904011 is composite: RES64: [76C1A61D4D910DFE]
- 10^999999+904017 is composite: RES64: [53837C5A256EE2D9]
- 10^999999+904137 is composite: RES64: [3A1A45B69770D52D]
- 10^999999+904189 is composite: RES64: [21C94E18189E34E1]
- 10^999999+904273 is composite: RES64: [0A6C775542764EE3]
- 10^999999+904339 is composite: RES64: [B0B23014CD954FD9]
- 10^999999+904389 is composite: RES64: [7C3432C206519C7F]
- 10^999999+904393 is composite: RES64: [6580278888B617E6]
- 10^999999+904419 is composite: RES64: [B30FCE1E2816ADB8]
- 10^999999+904431 is composite: RES64: [7EB296B17BBB7485]
- 10^999999+904717 is composite: RES64: [11BDF18FF27A3F21]
- 10^999999+904741 is composite: RES64: [1F64449C2721446F]
- 10^999999+904873 is composite: RES64: [43DA5854AE3DAF5A]
- 10^999999+904951 is composite: RES64: [4B84E5E5E1FF2A12]
- 10^999999+905011 is composite: RES64: [C0B1CDBD36124E05]
- 10^999999+905067 is composite: RES64: [1BE1D44590D75C74]
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- 10^999999+905293 is composite: RES64: [CAD66C0948BFC63C]
- 10^999999+905299 is composite: RES64: [8E68E4D71200652B]
- 10^999999+905307 is composite: RES64: [F15DB3C78C496573]
- 10^999999+905319 is composite: RES64: [C41810169ACE69F9]
- 10^999999+905349 is composite: RES64: [0A6EEBE46DDA01F9]
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- 10^999999+905569 is composite: RES64: [1C46DE1FC5B522BE]
- 10^999999+905623 is composite: RES64: [6E74F2B8D1565475]
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- 10^999999+905691 is composite: RES64: [F537AC7F3C0463B6]
- 10^999999+905701 is composite: RES64: [247CB2824C68CD77]
- 10^999999+905869 is composite: RES64: [917E310B21A1D1FC]
- 10^999999+905931 is composite: RES64: [8F26ADDBE9445377]
- 10^999999+905977 is composite: RES64: [AEB3EED6EE1DF897]
- 10^999999+905991 is composite: RES64: [1C18FC2A1A5E8427]
- 10^999999+906043 is composite: RES64: [436A9A64622AEBAD]
- 10^999999+906051 is composite: RES64: [466BD8258F510315]
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- 10^999999+906463 is composite: RES64: [B483104BB6E33D37]
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- 10^999999+906541 is composite: RES64: [93478BFBB408E4D1]
- 10^999999+906583 is composite: RES64: [5BA501874CF2EECE]
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- 10^999999+910161 is composite: RES64: [681A36C03024D1EB]
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- 10^999999+922653 is composite: RES64: [1ABFB5965CC6D49C]
- 10^999999+922801 is composite: RES64: [7013AB125E8C683C]
- 10^999999+922837 is composite: RES64: [EB16832C8FE743BF]
- 10^999999+922891 is composite: RES64: [F370A05761338E53]
- 10^999999+922981 is composite: RES64: [63520B6797E5097C]
- 10^999999+922987 is composite: RES64: [FA95B2C3879AFCB3]
- 10^999999+923061 is composite: RES64: [20883E145473F79E]
- 10^999999+923103 is composite: RES64: [4CFBDC141745B4F3]
- 10^999999+923181 is composite: RES64: [C6EE83BB1FD86958]
- 10^999999+923239 is composite: RES64: [1906EAAF3F7EB2C9]
- 10^999999+923269 is composite: RES64: [F62DB1C9BACD7B69]
- 10^999999+923367 is composite: RES64: [9D457942A5A32766]
- 10^999999+923397 is composite: RES64: [2FF576F082AD9FF3]
- 10^999999+923463 is composite: RES64: [35DA03F86C4D7E41]
- 10^999999+923481 is composite: RES64: [5EA210921A8F3FD9]
- 10^999999+923533 is composite: RES64: [85E8CFDCCFB1E024]
- 10^999999+923769 is composite: RES64: [E47B4685394A96CF]
- 10^999999+923817 is composite: RES64: [68189CC8CCAB175E]
- 10^999999+923821 is composite: RES64: [C9EEBC1C08AACA6A]
- 10^999999+923829 is composite: RES64: [91AC4B1610C415B0]
- 10^999999+923871 is composite: RES64: [C2A3C31DBFAD2C2D]
- 10^999999+923899 is composite: RES64: [5ECB62F8D66821E8]
- 10^999999+923907 is composite: RES64: [8E51B8F6B512D16D]
- 10^999999+924051 is composite: RES64: [463B909B22F1136F]
- 10^999999+924061 is composite: RES64: [C8D0E930930A27A4]
- 10^999999+924087 is composite: RES64: [83DE9BF672B506E3]
- 10^999999+924129 is composite: RES64: [8D2EB31BDCA9D6F3]
- 10^999999+924157 is composite: RES64: [18F2170E60F4EEA1]
- 10^999999+924201 is composite: RES64: [31413DA32D1592D0]
- 10^999999+924289 is composite: RES64: [2559ED6CDB666EA5]
- 10^999999+924297 is composite: RES64: [61E8B8A385346717]
- 10^999999+924343 is composite: RES64: [0BEA1E818A56B5C4]
- 10^999999+924367 is composite: RES64: [8AF01D7ED372E542]
- 10^999999+924391 is composite: RES64: [ACEDB69CE8736E24]
- 10^999999+924453 is composite: RES64: [47553DF2B1386F9D]
- 10^999999+924469 is composite: RES64: [666F30DA0EBCBBCC]
- 10^999999+924471 is composite: RES64: [02DA867F105E9B6D]
- 10^999999+924571 is composite: RES64: [B1DE221C9269AE8D]
- 10^999999+924577 is composite: RES64: [CAFAFA33351EB5C0]
- 10^999999+924607 is composite: RES64: [6D23BFF8C81B4CBC]
- 10^999999+924781 is composite: RES64: [4D5907D7FE3FF289]
- 10^999999+924789 is composite: RES64: [D22F0CE6584F20F1]
- 10^999999+924801 is composite: RES64: [3E884840EE046EF3]
- 10^999999+924823 is composite: RES64: [9AA4D87E707CE806]
- 10^999999+924901 is composite: RES64: [F57C8343EF81C008]
- 10^999999+924933 is composite: RES64: [9150734102713D2E]
- 10^999999+924943 is composite: RES64: [D1F321E66F9EE6F5]
- 10^999999+925039 is composite: RES64: [3BD9A75D304F4302]
- 10^999999+925059 is composite: RES64: [46C3C3014375DD38]
- 10^999999+925143 is composite: RES64: [C37C451B180C0DC9]
- 10^999999+925267 is composite: RES64: [7729BF7E53E781C6]
- 10^999999+925279 is composite: RES64: [51E4BA3AB716CE33]
- 10^999999+925371 is composite: RES64: [DF9439E71BC646CE]
- 10^999999+925381 is composite: RES64: [30ADE9D2CC2DD557]
- 10^999999+925603 is composite: RES64: [D601C2EE83242CC2]
- 10^999999+925701 is composite: RES64: [AC2E6A9A5068AE43]
- 10^999999+925741 is composite: RES64: [029331E9F7A252D9]
- 10^999999+925819 is composite: RES64: [0FB8AFA85F6C4BEB]
- 10^999999+925903 is composite: RES64: [F29C0867CC9A7993]
- 10^999999+925917 is composite: RES64: [356716897C2BD896]
- 10^999999+926053 is composite: RES64: [0A49ADE413A676DA]
- 10^999999+926139 is composite: RES64: [FC44D3951062027D]
- 10^999999+926167 is composite: RES64: [1FDEBAF752F37FE5]
- 10^999999+926169 is composite: RES64: [65E1A7F4EFA1347E]
- 10^999999+926217 is composite: RES64: [14291B34C994BD3A]
- 10^999999+926229 is composite: RES64: [86C0B26B591F58A4]
- 10^999999+926263 is composite: RES64: [1C3C2404DB30C424]
- 10^999999+926337 is composite: RES64: [45B7F39EF363AEAE]
- 10^999999+926361 is composite: RES64: [823395AFD93BD368]
- 10^999999+926371 is composite: RES64: [A279EFB04C01E8D5]
- 10^999999+926529 is composite: RES64: [BA9C1F2FBB73FB36]
- 10^999999+926557 is composite: RES64: [842B7BFA9F9791C5]
- 10^999999+926583 is composite: RES64: [1DC8B83A8DE9D24E]
- 10^999999+926637 is composite: RES64: [70BFD751E99399AC]
- 10^999999+926643 is composite: RES64: [A4345ACE6917D9D8]
- 10^999999+926659 is composite: RES64: [FE38DDDA03D53B24]
- 10^999999+926677 is composite: RES64: [7544C895E7469E74]
- 10^999999+926767 is composite: RES64: [2152E27A6C074AF1]
- 10^999999+926851 is composite: RES64: [0FA70D269F582F5C]
- 10^999999+926937 is composite: RES64: [AEDB561FB097D4DE]
- 10^999999+927019 is composite: RES64: [250710C96CFD225E]
- 10^999999+927069 is composite: RES64: [F7DA439AE425CAB7]
- 10^999999+927141 is composite: RES64: [6EEF5DAFDCF58A4F]
- 10^999999+927199 is composite: RES64: [34F6B6EB45F2564D]
- 10^999999+927261 is composite: RES64: [CDDA80ACE086417B]
- 10^999999+927273 is composite: RES64: [3935042635AC32A2]
- 10^999999+927313 is composite: RES64: [456EC5A5FF2AE41D]
- 10^999999+927363 is composite: RES64: [BE58A09941AE3911]
- 10^999999+927399 is composite: RES64: [2102CD885FD15D10]
- 10^999999+927489 is composite: RES64: [374831A76FC667CB]
- 10^999999+927511 is composite: RES64: [1A3B52B155C02BCF]
- 10^999999+927601 is composite: RES64: [62CAA392E170A7BF]
- 10^999999+927607 is composite: RES64: [1BB7EED117799B47]
- 10^999999+927789 is composite: RES64: [306C7D9BC0519864]
- 10^999999+927819 is composite: RES64: [3D3239F730416FD5]
- 10^999999+927849 is composite: RES64: [C41A8FF35BED5424]
- 10^999999+927861 is composite: RES64: [4C2D7A8EC21B3556]
- 10^999999+927901 is composite: RES64: [1B37603110DC7494]
- 10^999999+927943 is composite: RES64: [FC3EDAE0B96B039A]
- 10^999999+927973 is composite: RES64: [47379FA249D671B3]
- 10^999999+927997 is composite: RES64: [05223F9B722E2A93]
- 10^999999+928017 is composite: RES64: [A8E6CA21807A2120]
- 10^999999+928053 is composite: RES64: [0CBBE2590346BA26]
- 10^999999+928221 is composite: RES64: [42946285A10D20DA]
- 10^999999+928233 is composite: RES64: [9123607FA31AECAD]
- 10^999999+928287 is composite: RES64: [19FC661D40B70758]
- 10^999999+928321 is composite: RES64: [C8FAC6C42A1E2AF8]
- 10^999999+928323 is composite: RES64: [1D27BE283AF22EF0]
- 10^999999+928399 is composite: RES64: [A38933E7EF7C647B]
- 10^999999+928459 is composite: RES64: [C93027308C62552A]
- 10^999999+928471 is composite: RES64: [5D1B258B6FC01357]
- 10^999999+928701 is composite: RES64: [7FE6E51A88A39ED6]
- 10^999999+928707 is composite: RES64: [13FCB04FCC0A15A8]
- 10^999999+928843 is composite: RES64: [F40BABD7B224F14E]
- 10^999999+928867 is composite: RES64: [D48BB04D5DC6329A]
- 10^999999+928891 is composite: RES64: [19719D34D6A490D8]
- 10^999999+928909 is composite: RES64: [282705F159BD6165]
- 10^999999+928977 is composite: RES64: [5747593C9796799F]
- 10^999999+928993 is composite: RES64: [560BD1D7E084D95F]
- 10^999999+929001 is composite: RES64: [E47743EBA74B6E10]
- 10^999999+929047 is composite: RES64: [98298D740418FB0E]
- 10^999999+929067 is composite: RES64: [9E724C53994D336B]
- 10^999999+929323 is composite: RES64: [5936E9672B38CF8A]
- 10^999999+929473 is composite: RES64: [7D234A20E43C5146]
- 10^999999+929509 is composite: RES64: [2F882E262E898C3D]
- 10^999999+929511 is composite: RES64: [AAD571BFDE965BCC]
- 10^999999+929551 is composite: RES64: [645A64F87F073AB9]
- 10^999999+929689 is composite: RES64: [3CF61ECAC597789D]
- 10^999999+929697 is composite: RES64: [B956BDDCDA30B3C0]
- 10^999999+929703 is composite: RES64: [1B6E2F0CD7F59D5C]
- 10^999999+929719 is composite: RES64: [3F89AB25A3F3286A]
- 10^999999+929751 is composite: RES64: [3CE1AB9F904966DC]
- 10^999999+929863 is composite: RES64: [7658B06676D4586E]
- 10^999999+929877 is composite: RES64: [E3680A4887297D2B]
- 10^999999+929929 is composite: RES64: [52693124272FE512]
- 10^999999+944449 is composite: RES64: [D06FA90883783875]
- 10^999999+947749 is composite: RES64: [AEDD784DC8AF7A38]
- 10^999999+948849 is composite: RES64: [FCD45CB18A3BBDAB]
- 10^999999+954459 is composite: RES64: [3596E3737DDC2A97]
- 10^999999+965569 is composite: RES64: [ED1A8CE1495CA144]
- 10^999999+986689 is composite: RES64: [4CB7CD4DC153AFE7]
- 10^999999+987789 is composite: RES64: [1BB4A4D3ACF670CD]
- 10^999999+1015101 is composite: RES64: [8F4F918E087FC0E5]
- 10^999999+1040401 is composite: RES64: [60DFEB0F0455C529]
- 10^999999+1048401 is composite: RES64: [5397778510F173C9]
- 10^999999+1057501 is composite: RES64: [188A8275D4C66C3F]
- 10^999999+1070701 is composite: RES64: [AD982B4718374336]
- 10^999999+1105011 is composite: RES64: [0ACA6631C2CD2429]
- 10^999999+1113111 is composite: RES64: [D546C8B048940E8A]
- 10^999999+1168611 is composite: RES64: [788462DBA209AF8B]
- 10^999999+1204021 is composite: RES64: [29F5631937C4F3E1]
- 10^999999+1225221 is composite: RES64: [141D11E86E658AF7]
- 10^999999+1234321 is composite: RES64: [E50B1F6F1E95C3CD]
- 10^999999+1280821 is composite: RES64: [CB2CB6D77399B7A1]
- 10^999999+1321231 is composite: RES64: [318A1FB64209CD31]
- 10^999999+1368631 is composite: RES64: [6D4FEB045338FFDB]
- 10^999999+1387831 is composite: RES64: [A82172DE961C2646]
- 10^999999+1400041 is composite: RES64: [020913A559820878]
- 10^999999+1419141 is composite: RES64: [245FF6776F3C9B3E]
- 10^999999+1476741 is composite: RES64: [7C511DC49A19FFA3]
- 10^999999+1485841 is composite: RES64: [03067C6B0E22896B]
- 10^999999+1498941 is composite: RES64: [B7370AA0DAB6B6F8]
- 10^999999+1553551 is composite: RES64: [5F744745D4CBE4D9]
- 10^999999+1578751 is composite: RES64: [7A71F9842AB6A620]
- 10^999999+1654561 is composite: RES64: [C50845FDB5906F6A]
- 10^999999+1675761 is composite: RES64: [2DA27E8F866CF3FE]
- 10^999999+1687861 is composite: RES64: [58BE327069F7E986]
- 10^999999+1757571 is composite: RES64: [1E003D1DAEBE2279]
- 10^999999+1793971 is composite: RES64: [9DC71B6C6B1ED286]
- 10^999999+1800081 is composite: RES64: [C074C0ABFEC80D8E]
- 10^999999+1852581 is composite: RES64: [A6D152C186D6927A]
- 10^999999+1867681 is composite: RES64: [812EE7FAB5661D10]
- 10^999999+1907091 is composite: RES64: [16ECCE5BA73CDFC7]
- 10^999999+1951591 is composite: RES64: [B50D9F5FD040EBA0]
- 10^999999+1953591 is composite: RES64: [3C93CA6E1BA68E35]
- 10^999999+3003003 is composite: RES64: [4A4D310F8B81DB51]
- 10^999999+3012103 is composite: RES64: [A630B49EF7E8DF04]
- 10^999999+3053503 is composite: RES64: [690100B7D341F895]
- 10^999999+3063603 is composite: RES64: [462712F1EBA189A1]
- 10^999999+3071703 is composite: RES64: [A5196D3431A31155]
- 10^999999+3085803 is composite: RES64: [BB4C500BB72BCA61]
- 10^999999+3086803 is composite: RES64: [4970C8EC5BA013C7]
- 10^999999+3089803 is composite: RES64: [BF856DCE0F375AB8]
- 10^999999+3104013 is composite: RES64: [1594CF61C25EF82D]
- 10^999999+3129213 is composite: RES64: [8D2CCAC7C6BF02EF]
- 10^999999+3205023 is composite: RES64: [AB5FB16635577501]
- 10^999999+3258523 is composite: RES64: [31C6E4A59827213A]
- 10^999999+3290923 is composite: RES64: [390C251218B2D2E4]
- 10^999999+3292923 is composite: RES64: [9194F58D53F50F33]
- 10^999999+3336333 is composite: RES64: [BADECEE33FCE0AF9]
- 10^999999+3350533 is composite: RES64: [938E575716EEB27F]
- 10^999999+3374733 is composite: RES64: [91E75F36FA523E4D]
- 10^999999+3388833 is composite: RES64: [28C98073A90D8212]
- 10^999999+3394933 is composite: RES64: [A24C12ECB76A27D0]
- 10^999999+3401043 is composite: RES64: [6A372A35E68F09B8]
- 10^999999+3410143 is composite: RES64: [F411A379D87458C0]
- 10^999999+3413143 is composite: RES64: [C8A789CCAE41A771]
- 10^999999+3426243 is composite: RES64: [D3395E2FD11E2907]
- 10^999999+3435343 is composite: RES64: [0C6A9A3D3707AF84]
- 10^999999+3450543 is composite: RES64: [50BA6016E904B8E7]
- 10^999999+3461643 is composite: RES64: [CB49CA7A7425C78B]
- 10^999999+3464643 is composite: RES64: [4FE71779177705E5]
- 10^999999+3498943 is composite: RES64: [AA284780F62DD155]
- 10^999999+3502053 is composite: RES64: [143AD3E9C19DEEB1]
- 10^999999+3510153 is composite: RES64: [623451A3A0B522E9]
- 10^999999+3540453 is composite: RES64: [325F52265537A583]
- 10^999999+3584853 is composite: RES64: [863483E445AE53A0]
- 10^999999+3637363 is composite: RES64: [AEBB51146CB0657D]
- 10^999999+3659563 is composite: RES64: [AD22265F5A2A164C]
- 10^999999+3663663 is composite: RES64: [B26961498016374E]
- 10^999999+3664663 is composite: RES64: [7C316E8D4832ADE4]
- 10^999999+3680863 is composite: RES64: [EFDF1774044B891C]
- 10^999999+3708073 is composite: RES64: [7F9A55343EA07A44]
- 10^999999+3713173 is composite: RES64: [E9541B204BE249AA]
- 10^999999+3749473 is composite: RES64: [52410C32AEF397CE]
- 10^999999+3756573 is composite: RES64: [8A35CC1F08BCF9D5]
- 10^999999+3767673 is composite: RES64: [598803B5D15DBF3F]
- 10^999999+3866683 is composite: RES64: [ECDFD20656D3EBD3]
- 10^999999+3874783 is composite: RES64: [F92DE97B7AE356FA]
- 10^999999+3898983 is composite: RES64: [9E62EBFF2D9B7230]
- 10^999999+3906093 is composite: RES64: [D0CFF69267F8B0AE]
- 10^999999+3928293 is composite: RES64: [F7E8AF6F0EE04DB4]
- 10^999999+3933393 is composite: RES64: [B5671E6809C84A3F]
- 10^999999+3939393 is composite: RES64: [9014AC52D9F9DFAB]
- 10^999999+3967693 is composite: RES64: [BC3CA8CE69570834]
- 10^999999+3988893 is composite: RES64: [F183446A924B1A25]
- 10^999999+3994993 is composite: RES64: [C2B59EF69F21B0EB]

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Patrick De Geest - Belgium - Short Bio - Some Pictures

E-mail address : pdg@worldofnumbers.com