Challenge

[science_man_88]

if you look at wikipedia the double mersenne primes go:

7, 127, 2147483647, 170141183460469231731687303715884105727
first all of them end in 7
next if you look at the table for mersenne primes they have:

p Mp
3 7
7 127
127 170141183…884105727

If I'm right in assuming the last Mp is the last in this series and this pattern continues( the pattern is Mp becomes the next p) then the next one in this sub series( or what ever you want to call it) is:

p
170141183460469231731687303715884105727

Mp
2^170,141,183,460,469,231,731,687,303,715,884,105, 727-1


if this is true it smashes all records as the biggest prime to date and biggest mersenne prime is 2^46 million and something this is 2^ 170 Undecillion and something.

I left gimps as it took to much time for me. but can anyone confirm this pattern or try it out if so it would be the biggest known prime.

[science_man_88]

Oh by the way it might take 21 tera tera tera bytes to write in binary form but anyone willing to try ?

[science_man_88]

oh if you look at it the pattern would be
(2^3)-1,(2^7)-1,(2^2^7)-1,(2^2^2^7)-1,(2^2^2^2^7)-1,..........................................................................................................

[lfm]

Originally Posted by science_man_88

if you look at wikipedia the double mersenne primes go:

7, 127, 2147483647, 170141183460469231731687303715884105727
first all of them end in 7
next if you look at the table for mersenne primes they have:

No one knows if the 3rd exponent yields a prime let alone the 4th. This is just someone's wild speculation.

[science_man_88]

actually it's a pattern I saw as a possibility in the table but if you don't want to find out if M170,141,183,460,469,231,731,687,303,715,884,105,727 is prime

[science_man_88]

2^3 = 8-1 = 7
2^7 = 128-1=127
2^127(messed up before) = 170141183460469231731687303715884105728-1=170141183460469231731687303715884105727
2^170141183460469231731687303715884105727-1 ?

[Dougal]

it is impossible to confirm with todays technology.the only thing that can be done is confirm it is not prime.this can be done by trial factoring it with a program such as factor 5.it has already been trial factored up to around 170 bits without a factor.

[lfm]

Originally Posted by science_man_88

2^3 = 8-1 = 7
2^7 = 128-1=127
2^127(messed up before) = 170141183460469231731687303715884105728-1=170141183460469231731687303715884105727
2^170141183460469231731687303715884105727-1 ?

We would like to know I suppose but we are not going to find out any time soon without some breakthrough in the math. It is simply too large to test with any known method of testing primes.

The record is 2^43112609 - 1 that was discovered last year by the GIMPS projects.

[lfm]

Originally Posted by Dougal

it is impossible to confirm with todays technology.the only thing that can be done is confirm it is not prime.this can be done by trial factoring it with a program such as factor 5.it has already been trial factored up to around 170 bits without a factor.

I think it is too large for factor5 too. I suppose it could be tested for factors with some relatively simple new software but it doesn't realy seem worth the effort at this time.

[Dougal]

M170141183460469231731687303715884105727,MM127 can be tested with factor5.he also mentions MM31,i thought there was a factor found for it?

[flouran]

Does science_man_88 = ? I am not sure yet, as I have not had much experience with the and related creatures.
Anyone agree/beg to differ?
If so, I vote that this thread should be moved to Miscellaneous Math.