[QUOTE=alpertron;374996]I found that there are some holes in the PRP database on [url]http://www.mersenne.ca[/url]. For example, from the link: [url]http://www.mersenne.ca/prp.php?show=2&min_exponent=1828000&max_exponent=1911149[/url] we can find a lot of exponents without PRP done, but this range cannot be reserved using the form [url]http://www.mersenne.ca/prp.php?show=3&min_exponent=1828000&max_exponent=1911149[/url][/QUOTE]

The "no"s at your first link mean that a PRP test was run and determined it was composite, not that no test has been run. I don't see any gaps here.

There are thousands of exponents that have no "no" or "PRP" in that range, so the result is unknown from the point of view of the database.

[QUOTE=alpertron;374999]There are thousands of exponents that have no "no" or "PRP" in that range, so the result is unknown from the point of view of the database.[/QUOTE]

Oh, I see what you mean. Mea culpa. Assuming all is working as intended, the only apparent cause, then, is that they're reserved to be PRP tested. It says the reservations last for 7 days, so they should soon be complete or available for reservation.

I've just found a complete factorization:

M576551 = 4612409 x 64758208321 x 242584327930759 x PRP-173528

Congrats! Please submit it to Henri Lifchitz's PRP database. :smile:

[QUOTE=paulunderwood;375751]Congrats! Please submit it to Henri Lifchitz's PRP database. :smile:[/QUOTE]
I've just did that, thanks.

[QUOTE=alpertron;375749]I've just found a complete factorization:

M576551 = 4612409 x 64758208321 x 242584327930759 x PRP-173528[/QUOTE]

Just to be pedantic, if it's a PROBABLE prime factor then all we know for certain is that we don't actually know the answer :grin:

For a moment there got quite [U]excited [/U]when I saw completely factored :mad:

[QUOTE=Gordon;375794]Just to be pedantic, if it's a PROBABLE prime factor then all we know for certain is that we don't actually know the answer :grin:

For a moment there got quite [U]excited [/U]when I saw completely factored :mad:[/QUOTE]Well since we are being pedantic :ermm: then it is easy to find completely factored Mersenne numbers much larger than any given here. For instance 2[sup]57885161[/sup]-1 is one such number. :evil:

And here is another: 2[sup]2[sup]26[/sup][/sup]-1. :razz:

[color=grey]All numbers presented here meet the definition of a Mersenne number as specified in the current title "New [b]mersenne number[/b] completely factorized".[/color]

[QUOTE=retina;375795]Well since we are being pedantic :ermm: then it is easy to find completely factored Mersenne numbers much larger than any given here. For instance 2[sup]57885161[/sup]-1 is one such number. :evil:

And here is another: 2[sup]2[sup]26[/sup][/sup]-1. :razz:

[color=grey]All numbers presented here meet the definition of a Mersenne number as specified in the current title "New [b]mersenne number[/b] completely factorized".[/color][/QUOTE]

Then there's that pesky thing called a dictionary :smile:

probable  
1. likely to occur or prove true
2. having more evidence for than against, or evidence that inclines the mind to belief but leaves some room for doubt.
3. affording ground for belief.

So by definition, it is not [U][B]completely[/B][/U] factored.

[QUOTE=retina;375795]2[sup]2[sup]26[/sup][/sup]-1[/QUOTE]
:orly emu:
This equals (2^2^25-1)(2^2^25+1).
Since when F25 is full factored? :shock:

[QUOTE=Gordon;375796]So by definition, it is not [U][B]completely[/B][/U] factored.[/QUOTE]I never said it was. But I did give larger examples that are.