[QUOTE=tuckerkao;592627]What test will be needed to confirm the probable prime from the cofactor of M[M]10443557[/M]? Is there 1 doable test like LL to the regular PRP?[/QUOTE]
The short answer is "no!". See [url]https://primes.utm.edu/prove/[/url] :smile: 
[QUOTE=masser;592613]I would like young Tucker to do some of the legwork himself.[/QUOTE]So would I. But if he were willing to do legwork himself, he would not have posted his query. I posted the links for the benefit of others. Back when I was a new user, I was advised to use "show single post" in referring to previous posts. Locating the page with a given post number in a long thread can be tedious.
But, just for fun, I will mention that two smaller p > 1000000 for which M[sub]p[/sub] has a large PRP cofactor are mentioned on this Forum, [i]somewhere[/i] in [url=https://www.mersenneforum.org/showthread.php?t=19157]this thread[/url], which is a predecessor to the present one. That thread is much shorter than this one. 
[QUOTE=Dr Sardonicus;592632]But, just for fun, I will mention that two smaller p > 1000000 for which M[sub]p[/sub] has a large PRP cofactor are mentioned on this Forum, [i]somewhere[/i] in [url=https://www.mersenneforum.org/showthread.php?t=19157]this thread[/url], which is a predecessor to the present one. That thread is much shorter than this one.[/QUOTE]
I saw 4 of them inside that thread: M[M]4187251[/M], M[M]4834891[/M], M[M]5240707[/M], M[M]7080247[/M]. Those are the 4 predecessors of M[M]10443557[/M] which is the current largest known PPRPCF. I wish there can be a new specialized page for Known Cofactor Probable Primes or Fully factored Mersenne Numbers that are not Mersenne Primes under Current Progress menu of the GIMPS homepage. The total quantity is scarce enough that qualifies to be the Mersenne treasures of the discoverers. 
[QUOTE=tuckerkao;592633]I wish there can be a new specialized page for Known Cofactor Probable Primes or Fully factored Mersenne Numbers that are not Mersenne Primes under Current Progress menu of the GIMPS homepage.[/QUOTE]
That sounds like it would be better under the Wiki. Why don't you step up, and curate that? Might reduce the noise here on the Forum. Just asking... 
[QUOTE=tuckerkao;592633]I wish there can be a new specialized page for Known Cofactor Probable Primes or Fully factored Mersenne Numbers that are not Mersenne Primes under Current Progress menu of the GIMPS homepage.[/QUOTE]
[url]https://www.mersenne.ca/prp.php[/url] 
Congrats to Gelly (Robert Gelhar) for proving prime the [URL="http://factordb.com/index.php?id=1100000000013690992"]cofactor of 2^1063911[/URL]

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