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2021-09-28, 00:25   #276
rudy235

Jun 2015
Vallejo, CA/.

1,097 Posts

Quote:
 Originally Posted by paulunderwood Congrats to James Winskill for the mega primorial prime: 3267113# - 1 (1,418,398 decimal digits).
Yes, in the last few days we have had two new categories of primes entering the megaprime territory. A Palindromic with 1,234,567 digits and this Primorial with 1,418,398 digits. The next one coming is probably the 3rd term of a Prime in A.P.

We now have close to 1,125 megaprimes

Last fiddled with by Dr Sardonicus on 2021-09-28 at 10:58 Reason: xingif posty

2021-09-28, 21:57   #277
Batalov

"Serge"
Mar 2008
Phi(4,2^7658614+1)/2

9,833 Posts

Quote:
 Originally Posted by rudy235 ...A Palindromic with 1,234,567 digits and ...

2021-09-29, 14:25   #278
paulunderwood

Sep 2002
Database er0rr

414810 Posts

Quote:
 Originally Posted by Batalov How about two of them?
You mean "two more"?

https://primes.utm.edu/primes/page.php?id=132766
https://primes.utm.edu/primes/page.php?id=132767

 2021-10-16, 17:50 #279 rudy235     Jun 2015 Vallejo, CA/. 1,097 Posts How difficult is to prove a primorial Prime? 3267113# - 1 Verification status (*): InProcess Is still unproven. I would think that having the primorial +1 100% factored would make proving it a matter of a couple of says. A week in the worse case.
2021-10-16, 17:54   #280
paulunderwood

Sep 2002
Database er0rr

22×17×61 Posts

Quote:
 Originally Posted by rudy235 How difficult is to prove a primorial Prime? 3267113# - 1 Verification status (*): InProcess Is still unproven. I would think that having the primorial +1 100% factored would make proving it a matter of a couple of says. A week in the worse case.
Some numbers require proof attempts at increasing sizes of FFT.

 2021-10-18, 22:55 #281 paulunderwood     Sep 2002 Database er0rr 10000001101002 Posts Two birds with one stone Congrats tp Ryan and Serge for the record Near-rep Digit / Palindrome prime 10^1888529 - 10^944264 - 1 Last fiddled with by paulunderwood on 2021-10-18 at 22:56
2021-10-18, 23:44   #282
Batalov

"Serge"
Mar 2008
Phi(4,2^7658614+1)/2

9,833 Posts

Quote:
 Originally Posted by paulunderwood Congrats tp Ryan and Serge for the record Near-rep Digit / Palindrome prime 101888529 - 10944264 - 1
Yet another custom sieve for such hybrid beasts:
quick sketch:

We are searching for NRP(K,n) = 102n+1-K*10n-1. K can only be 1,2,4,5,7,8. (K=3 has algebraic factorization, which is not needed ...because the whole expression is divisible by 3 when 3|K).

Step 1. Let x=10^n, then NRP(K,n) = 10x2-Kx-1 . I solve this quadratic equation just like in school but x is some Mod(x,p) then sieve by p

Step 2. If quadratic equation has solution (nearly half the time; if it doesn't , nothing to sieve out), then --

Step 3. Solve 10^n = x1 and 10^n = x2. This is called znlog() and these values will periodically repeat with period znorder().

Step 4. Sieve out and repeat for 7<= p <= 10^11 or 10^12.

Step 5: remove special cases for p={7,11,13} (this actually removes a huge fraction of candidates with K=2, that's why it is the "thinnest" K)

The trick is to code steps 1, 2 and 3, and to know how.

Step 6. Test. (we test all six number forms in order of size. The fact that K=1 produced the first hit is accidental. With K=1, the number looks a bit more elegant.)

2021-10-19, 01:14   #283
rudy235

Jun 2015
Vallejo, CA/.

1,097 Posts

Quote:
 Originally Posted by rudy235 How difficult is to prove a primorial Prime? 3267113# - 1 Verification status (*): InProcess Is still unproven. I would think that having the primorial +1 100% factored would make proving it a matter of a couple of days. A week in the worse case.
After 20 days (10/17/21) it was proven prime.

2021-10-20, 08:42   #284
sweety439

"99(4^34019)99 palind"
Nov 2016
(P^81993)SZ base 36

2·1,699 Posts

Quote:
 Originally Posted by Batalov Step 5: remove special cases for p={7,11,13} (this actually removes a huge fraction of candidates with K=2, that's why it is the "thinnest" K)
You mean that the Nash weight (or difficulty) for K=2 (999...9997999...999) is very low?

2021-10-22, 04:59   #285
Batalov

"Serge"
Mar 2008
Phi(4,2^7658614+1)/2

231518 Posts

Quote:
 Originally Posted by sweety439 You mean that the Nash weight ...
Dare you to define it (for these six sequences), but yes.
Quote:
 Originally Posted by sweety439 ... (or difficulty) for K=2 (999...9997999...999) is very low?
Dare you to define it (for these six sequences), but yes.

 2021-10-22, 08:20 #286 pepi37     Dec 2011 After milion nines:) 24·5·19 Posts If I may ask how many candidates remain after that ?

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