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## #1 2013-06-08 05:23:18

Stangerzv
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### New Prime Unless Someone Else found it:)

Consider this equation.

Where, n is an integer, Pt is a prime number and Ps is the resulting Prime.

For n=1

Ps=5, 7, 11, 23, 47, 59, 83, 107, 167, 179, 227, 263, 347, 359, 383 for Pt<200 A well known prime (http://oeis.org/A005385)

For n=2

A well known prime (http://oeis.org/A155841)

For n=3

Ps=17, 263 for Pt<200

For n=4

Ps=79, 1049, 17179869269, 30354201441027016733116592294117482916287606860189680019559568902170379456331383469 for Pt<200

For n=5

Ps=37, 78167, 11920928955078263, 186264514923095703299, 4656612873077392578311 for Pt<200

For n=6

Ps=789730223053602977, 293242067884135544935936513642647623193965101483 for Pt<200

For n=7

Ps=367 for Pt<200

For n=8

Ps=144115188075856043, 154742504910672534362390789, 12259964326927110866866776217202473468949912977468817957, 363419362147803445274 661903944002267176820680343659030140745099590319644056698961663095525356881782780381260803133088966767300814308669 for Pt<200

For n=9

Ps=101, 4783039, 2541865828459 for Pt<200

For n=10

Ps=1033, 100000000000000000000253, 100000000000000000000000000319, 100000000000000000000000000000000000000000000000000000000000000000
000000000000000000000000000000000000000000001243 for Pt<200

Last edited by Stangerzv (2013-06-08 10:48:17)

## #2 2013-06-08 10:59:34

Stangerzv
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### Re: New Prime Unless Someone Else found it:)

Some values for larger n:

For n=100000000

Ps={1000000000000000300000003}, {10000000000000000000000000000000000000000000000000000000000000000
000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000002300000023} for Pt<200

## #3 2013-06-09 05:02:41

phrontister
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### Re: New Prime Unless Someone Else found it:)

Hi Stangerzv,

For n=156000000000000000000000

At Pt=197, Ps=a 4570-digit prime:

"PrimeQ[ps]" in Mathematica says the number is prime.

Do you have any means of testing this number for primality? I tried the online Elliptic Curve Method at http://www.alpertron.com.ar/ECM.HTM, but gave up because it was taking forever.

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

## #4 2013-06-09 06:07:04

Stangerzv
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### Re: New Prime Unless Someone Else found it:)

Hi phrontister

I would try to run it on alpertron and maybe after 1-2 days I would get the answer.

## #5 2013-06-09 10:48:08

phrontister
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### Re: New Prime Unless Someone Else found it:)

Hi Stangerzv,

Overnight I found a larger prime than in my last post, this time for Pt=199:

For n=2340240773870584944725754

At Pt=199, Ps=a 4919-digit prime:

"PrimeQ[ps]" in Mathematica says the number is prime.

I'll try the alpertron test on it. Pity it's so slow, though...their Java app time doesn't compare at all with Mathematica's PrimeQ function, which only takes 20 seconds to determine that Ps is prime.

Last edited by phrontister (2013-06-09 10:51:29)

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

## #6 2013-06-09 11:42:13

Stangerzv
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### Re: New Prime Unless Someone Else found it:)

Hi phrontister

There is a primality software (open source) used by gimps to find the largest mersenne's prime. There is USD150,000 award for those who could find the 100,000,000 millions digit prime by electronic frontier. Since you are good at programming why not you try this software. I am looking for to find non-mersenne's prime. So far all biggest primes are mersenne numbers.

Last edited by Stangerzv (2013-06-09 11:42:55)

## #7 2013-06-10 01:58:28

Stangerzv
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### Re: New Prime Unless Someone Else found it:)

After 20h 14 mins 37s

{1110 569841 961736 521093 527020 321061 997637 323487 171183 916164 743035
890337 478305 626254 080227 459404 322209 157812 216425 509264 920965 225954
216452 814660 943212 732459 541390 782750 026232 133733 246934 155146 590841
811410 546270 679392 624264 117413 197437 484536 121492 118007 586229 922433
542359 267360 140967 814731 499057 585417 184901 893328 122999 044651 625494
638152 554456 608373 144186 988936 455348 214706 248421 696806 985296 814269
741497 769100 215242 886224 200235 468455 936000 000000 000000 000000 000000
000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000
000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000
000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000
000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000
000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000
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000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000
000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000
000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000
000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000
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000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000
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000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000
000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000
000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000
000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000
000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000
000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000
000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000
000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000
000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000
000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000
000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000
000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000
000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000
000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000
000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000
000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000
000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000
000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000
000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000
000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000
000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000
000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000
000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000
000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000
000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000
000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000
000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000
000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000
000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000
000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000
000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000
000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000
000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000
000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000
000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000
000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000
000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000
000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000
000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000
000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000
000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000
000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000
000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000
000000 000000 000000 000000 000000 000000 000000 000000 000000 000000 000000
000000 000000 000000 000000 000000 000000 000000 000000 000000 000030 732000
000000 000000 000197 is prime }

Last edited by Stangerzv (2013-06-10 02:32:05)

## #8 2013-06-10 02:14:51

Stangerzv
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### Re: New Prime Unless Someone Else found it:)

Hi phrontister

I think mathematica's PrimeQ function is the same with alpertron.

## #9 2013-06-10 13:03:01

Stangerzv
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### Re: New Prime Unless Someone Else found it:)

This one also a prime

## #10 2013-06-10 22:06:16

phrontister
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### Re: New Prime Unless Someone Else found it:)

Yes, I saw that from M's solution but I only posted the largest Pt<200 for n=156000000000000000000000.

Alpertron is still busy thinking (and has been for 35 hours) about the 4919-digit prime from my post #5. If that number is prime it will be quite a while yet for it to find that out, as it's only up to 22% completion.

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

## #11 2013-06-10 22:54:07

phrontister
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### Re: New Prime Unless Someone Else found it:)

#### Stangerzv wrote:

There is a primality software (open source) used by gimps to find the largest mersenne's prime...Since you are good at programming why not you try this software. I am looking for to find non-mersenne's prime. So far all biggest primes are mersenne numbers.

Thanks for that, Stangerzv, but I only have a passing interest in primes. In fact, I don't even know what a Mersenne prime is, and although I've heard the term I've never been curious enough about it to find out what it is.

I've just enjoyed tackling the challenges you've posted because of the puzzle-solving aspect and the practical opportunity they give me to learn some more about Mathematica.

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

## #12 2013-06-11 00:01:47

Stangerzv
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### Re: New Prime Unless Someone Else found it:)

I would run it on my computer as mine is core i5. I am learning mathematica/matlab/mathcad while looking for a solution too. Regarding Mersenne, he was a bishop not even a mathematician but his work in mathematics was/is known by many people and Mersenne's prime is the most famous and there are group of people working everyday on grid computing to get the latest largest prime (Mersenne's prime 2^p-1). They have more than 700,000 cpus in their grid computing group linking by online network. Finding the largest prime having more than 20 millions digits on my computer maybe would take more than 50-100 years:)

## #13 2013-06-11 00:15:24

phrontister
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### Re: New Prime Unless Someone Else found it:)

Thanks for the Mersenne info and link...I'll check it out.

Alpertron is now up to 23% after 37.4 hours. I'll keep it running.

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

## #14 2013-06-11 01:38:03

phrontister
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### Re: New Prime Unless Someone Else found it:)

Hi Stangerzv,

I'll keep it running.

I've changed my mind and have put it out of its misery (it was still showing 23%!!), as I need all my computer's resources for rendering a video.

I'll just accept Mathematica's word for it that the 4919-digit prime from my post #5 is prime, as its assessment of the 4570-digit prime you tested in alpertron is accurate.

Last edited by phrontister (2013-06-11 01:49:27)

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

## #15 2013-06-11 02:44:34

Stangerzv
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### Re: New Prime Unless Someone Else found it:)

Hi phrontister

Don't worry I would get the result by tomorrow, now it is 11% after 2hours 41mins.

## #16 2013-06-12 22:20:27

Stangerzv
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### Re: New Prime Unless Someone Else found it:)

After 22h 1m 53s

{30 398195 986259 526179 302633 268366 341776 895486 915223 261429 574719
664291 540660 885243 535785 201913 587451 484005 348788 275448 583272 837731
792151 379645 657141 289600 115327 481119 099892 899538 205041 658220 871131
340323 267671 045321 059211 448641 665276 423953 359467 071362 517048 972796
783208 151823 033442 569886 693949 797990 780274 538453 391806 301941 108378
980830 100565 371775 006873 093696 868688 016144 255230 898989 809567 050225
323275 607703 687762 522940 558683 847549 109358 444056 315584 569759 894895
853117 791274 592614 104409 709799 600529 731948 419730 544427 679776 748268
520895 415201 403259 373393 153404 826778 407181 864405 394786 619383 497885
310639 267898 281896 648296 344821 942234 374165 992885 817128 361179 945381
633928 341963 008409 672119 238504 813798 748701 731076 524233 995979 037135
112013 125089 076959 564708 774147 064248 510993 307813 545556 125029 063630
979454 419686 668368 980592 341743 713160 789823 477957 223366 959589 127709
726671 285337 561116 082429 436247 887131 802447 128809 437369 699808 236416
869486 011279 516397 879073 978825 828138 275898 121489 545055 153789 495298
287782 609756 668631 885428 887207 234165 953658 525093 608212 872829 817616
897872 825591 133767 686913 805120 000233 349286 160789 671527 704607 300416
169569 144323 105042 722426 422443 812131 001906 946132 244641 402701 017848
279768 066740 446802 951019 403917 681739 034847 620165 718209 525443 343139
990870 233188 838990 636652 079277 747702 635000 175449 494652 945197 943767
800497 721393 243171 942432 510181 204627 959054 426470 046416 189604 755487
709391 175160 202859 354352 214522 663126 515831 156580 635237 816371 163629
650321 830465 779640 038989 294097 778448 983549 727413 438363 623539 370582
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712346 253724 229575 965637 179055 416760 125602 635786 564289 272398 311639
028493 706691 689470 093804 171563 621093 318073 508780 679537 427403 712935
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929832 950837 286295 307803 731414 081797 117488 488706 987012 363659 584698
739201 491322 776827 131638 691915 759098 574221 662323 775660 641820 337557
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080022 020968 131833 980438 505859 535946 297895 549573 937851 837803 655367
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934283 410807 996100 667964 338757 346589 is prime }

## #17 2013-06-12 22:28:48

bobbym

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### Re: New Prime Unless Someone Else found it:)

Hi;

Yes, that checks out as prime. Congratulations!

In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

## #18 2013-06-12 23:07:22

phrontister
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### Re: New Prime Unless Someone Else found it:)

Hi Stangerzv,

Thanks for that...and I got my video done. Nice to have that large prime confirmed by a program that seems to be well regarded in the prime community.

After 22h 1m 53s...

Mathematica took just 21.344 seconds.

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

## #19 2013-06-12 23:09:33

bobbym

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### Re: New Prime Unless Someone Else found it:)

You could probably beat that too with an AKS algorithm. Using a webpage has got to be slower.

In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

## #20 2013-06-12 23:54:35

phrontister
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### Re: New Prime Unless Someone Else found it:)

Hi Bobby,

I did a quick research on AKS but now know less about it than before I started...far too many multi-syllable words for me.

I found this question and two responses, though (for whatever they're worth):-

Question:

A few years ago, it was proven that PRIMES is in P. Are there any algorithms implementing their primality test in Python? I wanted to run some benchmarks with a naive generator and see for myself how fast it is. I'd implement it myself, but I don't understand the paper enough yet to do that.

Response #1:

AKS is of great theoretical importance but its performance is terrible (Miller-Rabin is much better).

Response #2

Quick answer: no, the AKS test is not the fastest way to test primality. There are much much faster primality tests that either assume the (generalized) Riemann hypothesis and/or are randomized. (E.g. Miller-Rabin is fast and simple to implement.) The real breakthrough of the paper was theoretical, proving that a deterministic polynomial-time algorithm exists for testing primality, without assuming the GRH or other unproved conjectures.

#### bobbym wrote:

Using a webpage has got to be slower.

The alpertron website says, "Since all calculations are performed in your computer, you can disconnect it from the Internet while the factorization is in progress."

I know you know I haven't got much idea at all about any of this, so please forgive me if I've taken a wrong turn.

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

## #21 2013-06-13 00:01:18

bobbym

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### Re: New Prime Unless Someone Else found it:)

Hi;

The Miller Rabin is a probabilistic test and as such is not certain. But if I tell you that this number is prime with only a chance of .000000000000000001% of not being a prime, then you can feel very safe about it. They are right about AKS, it takes about an hour to prove the primality of a 1000 digit number on an old desktop.

I know about Dario's site, I use the other features and stick to Miller Rabin for primality. About the GRH? That is very difficult to understand.

In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.