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2021-10-22, 15:57
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#287 | |
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
2·4,931 Posts |
Quote:
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2021-10-22, 17:44
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#288 |
Aug 2020
79*6581e-4;3*2539e-3
2×52×11 Posts |
New Primorial Prime found
Recently a new -1 type primorial prime was found at PRPNet.
3267113# - 1 It has 1418398 digits, making it the largest known one. The last -1 primorial prime was found more than 9 years ago, so this is quite the finding. The last +1 primorial prime hit is from 2001 btw. 20 years ago. :D I think it's an interesting type of prime due to its involvement in Euclid's proof of the infinitude of primes. Not many people seem to hunt for them though and they seem somewhat scarce taking into account that N+-1 has lots of factors. MODERATOR NOTE: Moved to this thread, which already has this post and several followups related to this number. Last fiddled with by Dr Sardonicus on 2021-10-23 at 02:37 |
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2021-10-22, 18:03
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#289 | |
Sep 2002
Database er0rr
11×383 Posts |
Quote:
The rarity of these numbers might put the next beyond the powers of Batalov-Propper. MODERATOR NOTE: Moved to this thread, which already has this post and several followups related to this number. Last fiddled with by Dr Sardonicus on 2021-10-23 at 02:38 |
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2021-10-25, 17:34
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#290 | |
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Aug 2020
79*6581e-4;3*2539e-3
10001001102 Posts |
Thanks for moving the post.
Quote:
I always forget the estimate for the digit size of primorials but the FFT size remains very managable even up to 20,000,000# where it's 3M. So if anyone was willing to put some larger ressources towards primorials or factorials, I'm pretty sure it'll yield some nice results before ending up in GIMPS waters. |
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2021-10-25, 20:53
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#291 | |
Feb 2017
Nowhere
22×1,459 Posts |
Quote:
? 3267113/log(10) %1 = 1418889.1476543787883927627556683863802 As indicated above, 3267113# - 1 actually has 1418398 digits. The estimate is a consequence of the Prime Number Theorem, which gives the asymptotic estimate ln(pk#) = ln(2) + ln(3) + ... + ln(pk) ~ pk |
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2022-01-10, 19:42
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#292 |
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Sep 2002
Database er0rr
11×383 Posts |
288465! + 1
Congrats to René Dohmen for the new factorial prime 288465! + 1 (1,449,771 decimal digits)
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2022-01-10, 22:07
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#293 |
May 2009
Russia, Moscow
53348 Posts |
Seems that this prime was found outside of Factorial Prime Search by Primegrid.
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2022-01-10, 22:39
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#294 | |
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Sep 2002
Database er0rr
421310 Posts |
Quote:
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2022-01-10, 23:30
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#295 |
Jun 2015
Vallejo, CA/.
2·3·5·37 Posts |
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2022-01-11, 01:32
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#296 | |
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Mar 2019
23×5×7 Posts |
Quote:
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2022-01-11, 07:32
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#297 | |
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Jun 2015
Vallejo, CA/.
111010 Posts |
Quote:
I misread the post. |
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