20210928, 00:25  #276  
Jun 2015
Vallejo, CA/.
1161_{10} Posts 
Quote:
We now have close to 1,125 megaprimes Last fiddled with by Dr Sardonicus on 20210928 at 10:58 Reason: xingif posty 

20210928, 21:57  #277  
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
2^{4}×7^{2}×13 Posts 
Quote:


20210929, 14:25  #278 
Sep 2002
Database er0rr
7×23×29 Posts 

20211016, 17:50  #279 
Jun 2015
Vallejo, CA/.
2211_{8} 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. 
20211016, 17:54  #280  
Sep 2002
Database er0rr
7·23·29 Posts 
Quote:


20211018, 22:55  #281 
Sep 2002
Database er0rr
11075_{8} Posts 
Two birds with one stone
Congrats tp Ryan and Serge for the record Nearrep Digit / Palindrome prime 10^1888529  10^944264  1
Last fiddled with by paulunderwood on 20211018 at 22:56 
20211018, 23:44  #282  
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
2^{4}·7^{2}·13 Posts 
Quote:
quick sketch: We are searching for NRP(K,n) = 10^{2n+1}K*10^{n}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 3K). Step 1. Let x=10^n, then NRP(K,n) = 10x^{2}Kx1 . 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 = x_{1} and 10^n = x_{2}. 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.) 

20211019, 01:14  #283  
Jun 2015
Vallejo, CA/.
3^{3}×43 Posts 
Quote:


20211020, 08:42  #284  
"99(4^34019)99 palind"
Nov 2016
(P^81993)SZ base 36
47×79 Posts 
Quote:


20211022, 04:59  #285  
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
2^{4}·7^{2}·13 Posts 
Quote:
Quote:


20211022, 08:20  #286 
Dec 2011
After 1.58M nines:)
2·3^{3}·31 Posts 
If I may ask how many candidates remain after that ?

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