20181207, 02:02  #1 
May 2010
Prime hunting commission.
2^{4}·3·5·7 Posts 
records for primes
is there a list of records for the largest "random" primes ever discovered?
primes like this, for example: Code:
603174145752094582013717026896404708075695200061888275740347912686132908983076912951364116014048644080780955692362443280745657218075567353486762269085008456050044645237568700267765675637155099757211742917240791004903205625152309314304699426586676846234879151913802061712891194848272697216649646754717 Last fiddled with by 3.14159 on 20181207 at 02:06 Reason: clarify! 
20181207, 03:15  #2  
Jun 2015
Vallejo, CA/.
3·383 Posts 
Quote:
If that is what you mean there are primes of the form x^{y}+y^{x} where x is odd and y is even (or viceversa) and have no common factor. Or a*b^{c}± N where a and b are small numbers, c is an ordinary number and N is another ordinary number. (greater than1) An example of the first kind is 6753^{5122}+ 5122^{6753} of 25,050 digits Of the second kind is 2^{116224}+15905 of almost 35,000 digits. Both of these kinds of numbers are not easy to prove prime and need to use a "general method like ECPP to prove them prime. However, they are still easy to express with an arithmetical formula. However a number like this one that has over 34,000 digits cannot be expressed with a mathematical formula (a simple one that is) and also needs ECPP to prove it as prime. So I suggest you look at the list of primes proven by ECPP in the Chris Caldwell webpage and see what you can find. You can start here or here 

20181207, 05:25  #4  
Aug 2006
5,987 Posts 
Quote:
See also Henri & Renaud Lifchitz's PRP Top records for probableprimes, which are typically of no special form (but lack a primality proof). 

20181207, 22:24  #5  
Jun 2015
Vallejo, CA/.
3·383 Posts 
Quote:
34093 decimal digits 

20181207, 23:59  #6  
Feb 2017
Nowhere
1847_{16} Posts 
Quote:


20181208, 17:49  #7 
Sep 2009
2·1,213 Posts 
The server is doing something funny. If I click on http://www.ellipsa.eu/public/primo/f...57885161.html (the original link) I get
Code:
Forbidden You don't have permission to access /public/primo/files/picture57885161.html on this server. Apache/2.4.10 (Ubuntu) Server at www.ellipsa.eu Port 80 Checking on another computer while I have the link from Picture(57885161) open on this computer I get the same pattern. So it must be putting something, probably a cookie, onto the system when you click on the Picture(57885161) link (both computers connect through the same router so the server will see them coming from the same IP address. But the original link sometimes still works for a few seconds after closing the Picture(57885161) link. Curiouser and curiouser. Chris 
20181208, 23:39  #8  
May 2010
Prime hunting commission.
2^{4}·3·5·7 Posts 
Quote:
Code:
In[6]:= RandomPrime[{10^49, 10^50}] Out[6]= 27101114565622859841940858633057180407935116844491 Last fiddled with by 3.14159 on 20181208 at 23:43 Reason: clarify #2 

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