A yuge number
 

[URL="https://chat.stackexchange.com/transcript/message/47904165#47904165"][COLOR=#0066cc] (2^7891456-1)*10^2375565+2^7891455-1[/COLOR][/URL]


Is this number a probable prime or which is the smallest factor?

[QUOTE=enzocreti;501734]Is this number a probable prime[/quote]
Almost certainly not.
[QUOTE=enzocreti;501734] or which is the smallest factor?[/QUOTE]

Could be too big for us to find out.

Why don't you do a PRP test using PFGW and find out if it is (probable) prime or composite?

No factors till 32*10^9. Quitting my attempt.

[QUOTE=enzocreti;501734][URL="https://chat.stackexchange.com/transcript/message/47904165#47904165"][COLOR=#0066cc] (2^7891456-1)*10^2375565+2^7891455-1[/COLOR][/URL]


Is this number a probable prime or which is the smallest factor?[/QUOTE]

it won't have any factors in common with M3, M5,M11,M13, M283 , or M15413 to start. if it did then then the consecutive Mersenne numbers in question would have to share a factor. it also won't share factors with 2^15413+1 and a few other numbers. just using simple math.

Program
 

[QUOTE=axn;501741]No factors till 32*10^9. Quitting my attempt.[/QUOTE]

Can you tell me what program did you use?

[QUOTE=enzocreti;501848]Can you tell me what program did you use?[/QUOTE]

A quick 2-line throwaway script written in PARI/GP

code
 

[QUOTE=axn;501853]A quick 2-line throwaway script written in PARI/GP[/QUOTE]


Can you give me the code?

[QUOTE=enzocreti;501854]Can you give me the code?[/QUOTE]

Go write it for yourself. Prove to us that you are willing to do some actual work in proving your number schemes. We have been spoonfeeding your.

[CODE]mod_check(p)=my(r=Mod(2,p)^7891455); (r*2-1)*Mod(10,p)^2375565+r==1
forprime(p=2,,if(mod_check(p),print(p)))[/CODE]
Here you go...

code
 

[QUOTE=axn;501862][CODE]mod_check(p)=my(r=Mod(2,p)^7891455); (r*2-1)*Mod(10,p)^2375565+r==1
forprime(p=2,,if(mod_check(p),print(p)))[/CODE]Here you go...[/QUOTE]


ok thanks

Why not use Sage for that, though?