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Apart from your own biggest Prime, has anyone got a favourite Prime? Ok I'll go 1st. I like Van Z's gfn20. Not because it's the biggest but because of its symmetry, 919444. Just sits well on the tongue. Hard to forget. Ok maybe I'm mad or OCD but order has an elegance does it not?
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Van Zimmerman Volunteer moderator
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I like that one too. :) |
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I like that one too. :)
:) no you're not allowed, it's your biggest! Apart from your biggest! :)
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Van ZimmermanVolunteer moderator
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Ok, I would call out Tabaluga's 1955556^131072+1. Not so much for symmetry, but all those 5's. |
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Ok, I would call out Tabaluga's 1955556^131072+1. Not so much for symmetry, but all those 5's.
Now you're talking, that's exactly what I mean. I'm with you on that. :)
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 Crun-chiVolunteer tester
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To put aside it is (still) my largest prime, but when I found it it was like dream come true.
9*10^1009567-1 or 8 at the start and 9 up to the end, but there is 1009566 nines to the end :)
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271643232^131072+1 GENERALIZED FERMAT :)
93*10^1029523-1 REPDIGIT PRIME
31*332^367560+1 CRUS PRIME
Proud member of team Aggie The Pew. Go Aggie! |
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To put aside it is (still) my largest prime, but when I found it it was like dream come true.
9*10^1009567-1 or 8 at the start and 9 up to the end, but there is 1009566 nines to the end :)
Awesome!, think your may win with that one hands down! Game over! Ah no, but that is ridiculously cool! :)
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Dave
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Me too in terms of repdigit. Though I am also interested in binary-look primes, especially if they're palindromic... |
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467917 · 2^1993429 - 1
My first T5k prime, and highest ranking prime at the time of finding prime. It was part of the rieselsieve project, and one of my systems found it on Christmas eve. I only found out when I checked my e-mail on Christmas day. Best present ever. |
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Me too in terms of repdigit. Though I am also interested in binary-look primes, especially if they're palindromic...
Any examples? Don't know much about this area.
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My lucky number's 10590941048576+1 and 5641491616384+1 (GFN-14 Consecutive Prime) |
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467917 · 2^1993429 - 1
My first T5k prime, and highest ranking prime at the time of finding prime. It was part of the rieselsieve project, and one of my systems found it on Christmas eve. I only found out when I checked my e-mail on Christmas day. Best present ever.
Timing counts. How big was it and when?
Speaking of timing, I was hunting for gfn17low on the 4th june. Switched back to gfn18 when I saw one in the pipe and bang 18! But I had been on 18 since march, only switched to 17 low on the 2nd June or so. Almost missed it :)
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Timing counts. How big was it and when?
https://primes.utm.edu/primes/page.php?id=76544
Just over 600k digits in 2005. Today, even a PPS prime would be bigger. I suppose you could put that prime down as the one that got me addicted. |
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Timing counts. How big was it and when?
https://primes.utm.edu/primes/page.php?id=76544
Just over 600k digits in 2005. Today, even a PPS prime would be bigger. I suppose you could put that prime down as the one that got me addicted.
2005? Well impressive for then! Moore's law has had many iterations since then so pc power was comparatively poor back then so fair play to you for getting it.
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My lucky number's 10590941048576+1 and 5641491616384+1 (GFN-14 Consecutive Prime) |
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How about 288larsons 86884666^16384+1 is pretty cool?
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My lucky number's 10590941048576+1 and 5641491616384+1 (GFN-14 Consecutive Prime) |
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Well aside from the FPS i've found I like 2.
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19249*2^13018586+1 . Yes, it made more interested in all these searches. |
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I have found numerous mega primes, an actual SGS prime, a large Fermat divisor, and my favorite prime number is...
2
It is the only even prime number. That is awfully special in my book. :)
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tng*Send message
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I have found numerous mega primes, an actual SGS prime, a large Fermat divisor, and my favorite prime number is...
2
It is the only even prime number. That is awfully special in my book. :)
I'll go with 2 as well -- same reason
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Me too in terms of repdigit. Though I am also interested in binary-look primes, especially if they're palindromic...
Any examples? Don't know much about this area.
Mersenne primes are all 1s in binary. Of course they are not searched here at PrimeGrid.
Many primes we search here have trivial binary expansions because they are based on a huge power of two. For example a 321 prime of the minus type is all 1s except for the second-most significant bit which is 0, so:
101111...11
And 321 plus type starts with 11 then has only 0s until it ends in a single 1, that is:
110000...001
Any Proth prime (PPS, EPS, MEGA) is similar; it has a short "arbitrary" word of initial digits (from the k), then a long string of 0s and a single 1 in the end.
/JeppeSN |
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I have many favorites, but the number F4 = 65537 is cool because it is thought to be the largest prime of the form 2^N + 1, and hence the last prime that needs only two 1s in its binary expansion. And in hexadecimal as well.
In decimal, GF(1,10) = 101 is thought to be the last prime with digit sum 2. No multidigt prime in base 10 can have a digit sum of 3. Many primes with decimal digit sum 4 can be found (expect infinitely many, A062339).
In the opposite direction, primes of decimal appearance 899999...9 was already mentioned by Crun-chi.
/JeppeSN |
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Crun-chiVolunteer tester
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In form k*10^n+1 my largest prime is 9×10^100613+1
But now I attacking on two fronts ( 4*10^n+1 and 9*10^n+1), so you can expect one ,bigger, soon :)
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271643232^131072+1 GENERALIZED FERMAT :)
93*10^1029523-1 REPDIGIT PRIME
31*332^367560+1 CRUS PRIME
Proud member of team Aggie The Pew. Go Aggie! |
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My favorite prime is 22699.
It's one of the remaining SoB k's and the one from the very first SoB task I had from PrimeGrid. I was very interested in the subject and made a lot of my own little research looking into divisors of 22699*2^n+1 and stuff.
But if you need more generic proof, why it's a good prime? Sure. Let's start from 2 being a quite unique prime and 69 being... let's say, a well known number.
Then 269 is prime.
Then 2269 is prime and so is 2699.
Finally, 22699 is prime.
Q. E. D. |
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My favorite prime (other than my GFN-19), is 193*2^3329782+1.
It's the only known mega prime that is a Fermat divisor.
I was the one who manually ran the Fermat divisor tests for that prime, so I clearly remember looking at the result on my screen and thinking, "Whoa... does that really say what I think it says???" :)
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My lucky number is 75898524288+1 |
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My favorite prime (other than my GFN-19), is 193*2^3329782+1.
It's the only known mega prime that is a Fermat divisor.
I was the one who manually ran the Fermat divisor tests for that prime, so I clearly remember looking at the result on my screen and thinking, "Whoa... does that really say what I think it says???" :)
You remind me of 3*2^382449+1!
Transpose mega into 100,000-digit.
I will never forget the "Whoa!!!".
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In decimal, GF(1,10) = 101 is thought to be the last prime with digit sum 2. No multidigt prime in base 10 can have a digit sum of 3.
You made me think! Since the 1st one sounds unproven, then assuming the 2nd one is correct possible solutions must have factors. Am I good enough to work out a proof myself?... so that would be numbers either starting 2 ending 1 with variable number of zeros in between, or starting 1, ending 1, with a 1 in between, each separated by variable numbers of zeros... |
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In decimal, GF(1,10) = 101 is thought to be the last prime with digit sum 2. No multidigt prime in base 10 can have a digit sum of 3.
You made me think! Since the 1st one sounds unproven, then assuming the 2nd one is correct possible solutions must have factors. Am I good enough to work out a proof myself?... so that would be numbers either starting 2 ending 1 with variable number of zeros in between, or starting 1, ending 1, with a 1 in between, each separated by variable numbers of zeros...
think about divisibility by 3 |
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My favorite prime (other than my GFN-19), is 193*2^3329782+1.
It's the only known mega prime that is a Fermat divisor.
I was the one who manually ran the Fermat divisor tests for that prime, so I clearly remember looking at the result on my screen and thinking, "Whoa... does that really say what I think it says???" :)
Good one! I wonder when that record will be beaten (by some PrimeGrid user for sure).
It is quite hard to imagine how huge megaprimes are, but try to think about the Fermat number whose primality status (composite!) is revealed by this number:
F_3329780 = 2^(2^3329780) + 1
/JeppeSN |
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My favorite prime is 22699.
It's one of the remaining SoB k's and the one from the very first SoB task I had from PrimeGrid. I was very interested in the subject and made a lot of my own little research looking into divisors of 22699*2^n+1 and stuff.
But if you need more generic proof, why it's a good prime? Sure. Let's start from 2 being a quite unique prime and 69 being... let's say, a well known number.
Then 269 is prime.
Then 2269 is prime and so is 2699.
Finally, 22699 is prime.
Q. E. D.
Very very cool.
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My lucky number's 10590941048576+1 and 5641491616384+1 (GFN-14 Consecutive Prime) |
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How about this one, just got overnight,
131400000^16384+1,
Tidy. :)
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My lucky number's 10590941048576+1 and 5641491616384+1 (GFN-14 Consecutive Prime) |
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It's the only known mega prime that is a Fermat divisor.
This also made me wonder:
What is the first Fermat number divisible by a megaprime? The first one that has a chance, is F_22.
And what is the last Fermat number divisible by a non-mega-prime (a prime that is too small to be a megaprime)? It must be less than F_3321922, because all factors of F_n are of form k*2^(n+2) + 1 with k>1. So all primes from F_3321922 and up have only megaprimes as prime divisors.
/JeppeSN |
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It's the only known mega prime that is a Fermat divisor.
This also made me wonder:
What is the first Fermat number divisible by a megaprime? The first one that has a chance, is F_22.
I had to think about that one for a moment. :)
I don't think any of the searches we're doing, or any of the software, would be useful in answering that question. Certainly, PFGW, when checking for Fermat divisors, finds divisors MUCH larger than the prime being checked. For a prime with a million digits, it's looking at Fermat numbers around F_3300000, not F_22.
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Please do not PM me with support questions. Ask on the forums instead. Thank you!
My lucky number is 75898524288+1 |
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So all primes from F_3321922 and up have only megaprimes as prime divisors.
Of course, I meant all Fermat numbers from F_3321922 and up have only megaprimes as prime divisors. /JeppeSN |
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It's the only known mega prime that is a Fermat divisor.
This also made me wonder:
What is the first Fermat number divisible by a megaprime? The first one that has a chance, is F_22.
I had to think about that one for a moment. :)
I don't think any of the searches we're doing, or any of the software, would be useful in answering that question. Certainly, PFGW, when checking for Fermat divisors, finds divisors MUCH larger than the prime being checked. For a prime with a million digits, it's looking at Fermat numbers around F_3300000, not F_22.
I agree! Methods like the one used by David Bessel (Elliptic Curves Method (ECM) with Prime95 software) to find the first factor of F_22, or similar, could be used to find one more small factor, or a couple more, and then the cofactor can be tested, and if we are extremely lucky, that huge cofactor will be prime, a megaprime, and we will have F_22 divisible by a megaprime.
It would be really sensational to have F_22 completely factored like that (no Fermat number greater than F_11 has been completely factored).
I do not think we could find a megaprime factor of a "small" Fermat number like F_22 in any other way than eliminating some small factors and having enough luck that the huge cofactor after that is prime(?).
That megaprime would be expressible only as:
F_22 / [(3853959202444067657533632211*2^24 +1)*(other small factor)*...]
/JeppeSN |
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My favorite number is the 26th Eisenstein-Mersenne Norm prime: 3^2237561+3^1118781+1
My second favorite is the prime partitions number of a number which is square: partitions(14881^2)
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My lucky number is Phi(4, 2^2396029-1)/2.
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6391936^131072+1 found by participant jess is a nice prime too. 6391936 is palindromic. |
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6391936^131072+1 found by participant jess is a nice prime too. 6391936 is palindromic.
Agreed! Like it. Might be best yet :) well for me anyway :)
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My lucky number's 10590941048576+1 and 5641491616384+1 (GFN-14 Consecutive Prime) |
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Ä°t is very rare. There are no another example of this property among gfn primes (except gfn14 and below I didnt checked them) May be there are other examples in other subprojects. This is a nice thread I think. Participants can discover interesting properties about their primes and share here. I like and I am interested in prime curios /The numbers which have interesting properties and related to primes. I noticed another nice example ;
9249*2^32767+1 a pps prime with 9868 digits. 32767=2^15-1 :)) 9249*2^(2^15-1)+1 is prime ! wow.
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3909127223745*2^1290000-1 is prime!
126055746^32768+1 is prime!
175894284^16384+1 is prime! (Private gfn server)
127511188^8192+1 is prime! (Private gfn server) |
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Dave
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Are there any golden sequential pandigitals e.g.123456789×2^n? Or k×2^[pandigit]? Another mini-conjecture. |
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e.g.123456789×2^n
123456789*2^1 - 1 is prime :P
Or k×2^[pandigit]?
I would imagine a number of this size would be difficult to check, since it would have at a minimum 37 million digits (123456789 * log10(2) +1 ~ 37,164,197), which is currently 10 million digits longer than the largest prime found. Perhaps in the future, but I wouldn't bank on making that sort of discovery anytime soon. I suppose there would "only" be 362 thousand numbers to check per k - 724 thousand if you wanted +1 and -1 - but it seems like a lot of work.
I think far more interesting would be a prime where the numbers come in order - something like 1 * 2^(345*678) - 9 or something. I haven't found any resources on them, and while I'd like to search for them, I'm unclear on the number theory of the divisors of the power of 2 and primality and that sort of thing. |
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mackerelVolunteer tester
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If you go to https://primes.utm.edu/primes/search.php and search for 123456789 in description, and hit the box for all primes then there are a handful containing that sequence. Makes me wonder, how far have people searched 123456789*2^n +/- 1 |
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If you go to https://primes.utm.edu/primes/search.php and search for 123456789 in description, and hit the box for all primes then there are a handful containing that sequence. Makes me wonder, how far have people searched 123456789*2^n +/- 1
Wow there's quite a few including
123456789123456789 · 105513 + 1
New subproject? :)
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My lucky number's 10590941048576+1 and 5641491616384+1 (GFN-14 Consecutive Prime) |
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I got this one, would have been a beaut, but alas not prime
2244422^524288+1 :(
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My lucky number's 10590941048576+1 and 5641491616384+1 (GFN-14 Consecutive Prime) |
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Crun-chiVolunteer tester
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If you go to https://primes.utm.edu/primes/search.php and search for 123456789 in description, and hit the box for all primes then there are a handful containing that sequence. Makes me wonder, how far have people searched 123456789*2^n +/- 1
Wow there's quite a few including
123456789123456789 · 105513 + 1
New subproject? :)
Home subproject: even this is Primegrid forum, and we are all members of Primegrid, dont be afraid to start new sieve, make your own project, find your own prime.Even Primegrid give you chance to find primes in many projects it is still and only just grain of sand on whole beach of primes. :)
123456789*2 ^n+/-1 is also interesting
or
11111111111*2^n +/-1
Possibilities are endless
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271643232^131072+1 GENERALIZED FERMAT :)
93*10^1029523-1 REPDIGIT PRIME
31*332^367560+1 CRUS PRIME
Proud member of team Aggie The Pew. Go Aggie! |
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Got this today 304442222^16384+1
Sweet! :) symmetry.
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My lucky number's 10590941048576+1 and 5641491616384+1 (GFN-14 Consecutive Prime) |
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Fav number is 7 and a prime. |
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Dad
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Mine is
555*2^3563328+1
because it's got 555 and it's my first (and only) Mega
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Tonight's lucky numbers are
555*2^3563328+1 (PPS-MEGA)
and
58523466^131072+1 (GFN-17 MEGA) |
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If we talk about the relatively small primes, my favourite from them is 333667. It's probably the largest unique period prime without digits 0 1 9. Also this is the largest prime divisor of the "magic number" 12345679 and of course 111111111. And for its "almost symmetry". |
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If we talk about the relatively small primes, my favourite from them is 333667. It's probably the largest unique period prime without digits 0 1 9. Also this is the largest prime divisor of the "magic number" 12345679 and of course 111111111. And for its "almost symmetry".
https://primes.utm.edu/curios/page.php/333667.html |
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19 -- I've just always thought it was a good number.
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Thanks!!!
What about primes that make numbers after 271129 non-Sierpinski? Really like them.
271169*2^1725+1 and 271463*2^1805+1 (so, between 271129 and 271577 there is nothing missed).
324169*2^15802+1 and 327679*2^24046+1 (the same thing about 322523 and 327737). |
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Timing counts. How big was it and when?
https://primes.utm.edu/primes/page.php?id=76544
Just over 600k digits in 2005. Today, even a PPS prime would be bigger. I suppose you could put that prime down as the one that got me addicted.
2005? Well impressive for then! Moore's law has had many iterations since then so pc power was comparatively poor back then so fair play to you for getting it.
looks over at the Apple //e that shares my desk with the computer I run PG on... (8700K/1080Ti)
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Historian by education, philosopher by inclination, contrarian by nature.
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Timing counts. How big was it and when?
https://primes.utm.edu/primes/page.php?id=76544
Just over 600k digits in 2005. Today, even a PPS prime would be bigger. I suppose you could put that prime down as the one that got me addicted.
2005? Well impressive for then! Moore's law has had many iterations since then so pc power was comparatively poor back then so fair play to you for getting it.
looks over at the Apple //e that shares my desk with the computer I run PG on... (8700K/1080Ti)
Apple iPad 2 As Fast As The Cray-2 Super Computer on LINPACK benchmark* (Phoronix, 2012)
* With recursive/parallel LU factorization on the iPad 2
- Cray-2 released 1985
- iPad 2 released 2011 |
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I'd rather have the Cray than any Apple product that wasn't designed by Woz.
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Historian by education, philosopher by inclination, contrarian by nature.
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I'd rather have the Cray than any Apple product that wasn't designed by Woz.
Good luck fitting the Cray on your desk beside the 8700K/1080Ti |
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Plenty of space in this room.
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Historian by education, philosopher by inclination, contrarian by nature.
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My favourite prime is 1327, because it has quite a large gap of 34 following it.
By the way my favourite number is 1001 because it is sphenic and palindromic. Still looking for the fabled sphenic prime though. |
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Still looking for the fabled sphenic prime though.
Not sure there's a joke i'm missing, but sphenic numbers are composite by definition. |
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Still looking for the fabled sphenic prime though.
Not sure there's a joke i'm missing, but sphenic numbers are composite by definition.
Yeah I have a fondness for oxymorons that sound more plausible on account of the obscurity of the words. "Sceptical omphalist" would be another example. |
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Yeah I have a fondness for oxymorons that sound more plausible on account of the obscurity of the words. "Sceptical omphalist" would be another example.
If you have a fondness for sphenic numbers, the wikipedia page for them needs updating. They have the largest sphenic number known as of Jan of 2018, but there's a new biggest prime since then.
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