Prime pages question

jasong · 2013-03-09, 04:39

Following is a copy of the listing of the largest 10 prime numbers known by the world at large. You'll notice that the first 6 have question marks, meaning it hasn't been absolutely 100% confirmed that they are the 43rd to 48th Mersenne primes. It HAS been confirmed that they're prime, and that they're Mersenne numbers, it just hasn't been confirmed that there aren't any Mersenne primes below them.

Now, my question is whether or not there's a technical reason why some have 2 question marks and some have only one. I understand that the 2 question marked ones are more in doubt, but is there some sort of hard and fast rule that determines when you take away one of the 2 question marks?

Quote:

1b 2^57885161-1 17425170 G13 2013 Mersenne 48??
2 2^43112609-1 12978189 G10 2008 Mersenne 47??
3 2^42643801-1 12837064 G12 2009 Mersenne 46??
4 2^37156667-1 11185272 G11 2008 Mersenne 45?
5 2^32582657-1 9808358 G9 2006 Mersenne 44?
6 2^30402457-1 9152052 G9 2005 Mersenne 43?
7 2^25964951-1 7816230 G8 2005 Mersenne 42
8 2^24036583-1 7235733 G7 2004 Mersenne 41
9 2^20996011-1 6320430 G6 2003 Mersenne 40
10 2^13466917-1 4053946 G5 2001 Mersenne 39

Dubslow · 2013-03-09, 06:45

Not all exponents below M48 have been tested once, which is what the ?? is supposed to mean. All first time tests below M47 were only recently completed, and the table merely hasn't been updated. (That is, 43-47 should all be ? while 48 should be ??.)

LaurV · 2013-03-09, 06:49

Quote:

Originally Posted by jasong

it just hasn't been confirmed that there aren't any Mersenne primes below them.

Technically, there ARE mersenne primes below them. 42 in number.
What was not been confirmed is that there aren't any unknown Mersenne primes below them.

ET_ · 2013-03-09, 08:09

Quote:

Originally Posted by LaurV

Technically, there ARE mersenne primes below them. 42 in number.
What was not been confirmed is that there aren't any unknown Mersenne primes below them.

Mersenne prime exponents maybe?

Luigi

LaurV · 2013-03-09, 08:16

Quote:

Originally Posted by ET_

Mersenne prime exponents maybe?

Luigi

woot? exponents are trillions of trillions of trillions of...
who's talking about exponents?

ET_ · 2013-03-09, 08:44

Quote:

Originally Posted by LaurV

woot? exponents are trillions of trillions of trillions of...
who's talking about exponents?

Romulan Interpreter?

Luigi

jasong · 2013-03-09, 12:04

Quote:

Originally Posted by LaurV

Technically, there ARE mersenne primes below them. 42 in number.
What was not been confirmed is that there aren't any unknown Mersenne primes below them.

lol, fine, I don't get an A+ for my post. But, honestly, did people really think I hadn't just accidentally left some terms out? :)

LaurV · 2013-03-09, 12:10

No, they don't. It was nitpicking. But it was fun, because it did collateral damages too

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2013-03-09, 06:45	#2
Dubslow Basketry That Evening! "Bunslow the Bold" Jun 2011 40<A<43 -89<O<-88 7221₁₀ Posts	Not all exponents below M48 have been tested once, which is what the ?? is supposed to mean. All first time tests below M47 were only recently completed, and the table merely hasn't been updated. (That is, 43-47 should all be ? while 48 should be ??.)

2013-03-09, 12:10	#8
LaurV Romulan Interpreter "name field" Jun 2011 Thailand 2²×23×109 Posts	No, they don't. It was nitpicking. But it was fun, because it did collateral damages too