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3:23 AM
plot for $\sum_{k=1}^{\infty} (-1)^k(^{2k}x)$
plot for $\sum_{k=0}^{\infty} (-1)^k(^{2k+1}x)$
@TheSimpliFire
 
 
16 hours later…
7:34 PM
@TheSimpliFire Hi
 
Hello Peter
 
Do you have time and a powerful computer ? Do you have any new number theory project ?
 
Neither :/
Do you?
 
OK, perhaps you can help me in this : How can I find out the largest known prime number of the form $2^a\cdot 3^b+1$ with positive integers $a,b$ ?
 
Can't find anything yet on Google
 
7:41 PM
maybe on Chris Caldwell's prime page ? I think, you can search for expressions on this site.
 
@Peter
97 9*2^5642513+1 1698567 L3432 2013 ()**
$a=5642513$ and $b=2$ gives the 97th largest known
76 3*2^6090515-1 1833429 L1353 2010 ()**
 
Wow, a huge prime ! Thank you.
C 94381 (show) 39^(39^3)+39^1521+1<94381> = 2298392548...99<94381>
Maybe, you can find a prime factor of this number ?
 
The 35th largest prime has the form $2^{10829346}\cdot3^1+1$
@Peter No time for computational work atm
 
Much larger ...
An even larger one ? Or is this the current champion ?
 
This is the best we have
 
8:00 PM
OK, thank you.
@TheSimpliFire Is the 28th largest prime actually missing ?
 
8:50 PM
@Peter Very possibly a typo. The table is supposed to show the 100 largest primes, but the final row is row 101 (so misalignment)
 
9:00 PM
I asked here and received an answer showing the 28th largest known prime which can be seen by downloading the list.
No idea however what the reason for this issue could be !
Maybe mailing Chris Caldwell clarifies it.
 

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