list of untouched exponents

how to get the list of all untouched exponents?

[Uncwilly]

If you mean all that have had no testing on them, that list is infinite. The exponents are all prime numbers, of which there are infinitely many.

What area are you concerned with, 'low', those that have not yet been LL tested? Or higher, those that have had no trial factoring effort?

[cheesehead]

Originally Posted by Unregistered

how to get the list of all untouched exponents?

Here's one way, though it's tedious:

Go to the Version 5 server (still in beta test) at http://v5www.mersenne.org/.

Click on "Exponent Status" under the "Results Queries" heading in the left-side column (that takes you to http://v5www.mersenne.org/report_exponent/).

There, you can get the current status (prime, factored, no factor below 2^xx, no factor to P-1 limits, verified LL-tested, unverified LL-tested) of up to 100 candidates at a time, within a range you specify.

(Currently, it won't report on exponents greater than 1,000,000,000.)

[Batalov]

Ostensibly (except for some legacy untouchable ranges where weird things happen sometimes), at this time, every exponent under 1,000,000,000 was touched.

(There were some untouched exponents even two monts ago. Then typical TF jobs were TF to 60 bits above 720,000,000; then 800,000,000+ then some lower ranges... But now the typical factoring jobs are TF from 60 to 64 bits in the 171,000,000+ range - http://v5www.mersenne.org/report_recent_cleared/ Apparenly, all was touched, otherwise server would have reassigned it to someone.)

If you will find some, it will be interesting in some sense.

[ET_]

If you look at Will Edgington's tables of factors, you'll see that the factors sequence grows for exponents well over 3 billions. I'm pretty sure Will did some factoring work (though at very low bit depth) on all of them.

Luigi

[R.D. Silverman]

Originally Posted by Unregistered

how to get the list of all untouched exponents?

Literally impossible. The list is infinite.

[davieddy]

Originally Posted by R.D. Silverman

Literally impossible. The list is infinite.

See post 2

[cheesehead]

Originally Posted by Batalov

Apparenly, all was touched, otherwise server would have reassigned it to someone.

Correct. Some folks did indeed do a systematic TF up to 2^60 on all unfactored exponents up to 1,000,000,000.

---

For those new to the idea of trial-factoring Mersennes with larger exponents than the few-million we've been used to discussing:

Note that TF up to 2^60 on an exponent around 999,000,000 is roughly a thousand times as fast than a TF to 2^60 on an exponent around 999,000. Why? Because the potential divisors are about a thousand times as far apart for the former than for the latter, as one can deduce from the 2kn+1 requirement, so there are only one one-thousandth as many to test in the range of factor sizes up to 2^60.

It's true that there's a logarithmic factor in individual trial-division times, but that's much less significant than the linear-with-exponent decrease in number of potential candidates to be tested.

[ckdo]

Originally Posted by cheesehead

Correct. Some folks did indeed do a systematic TF up to 2^60 on all unfactored exponents up to 1,000,000,000.

Most have actually only been TF'd to 2⁵⁶. Getting them all to 2⁶⁰ is a task which will take months, if not years, to complete.

[S485122]

Originally Posted by ckdo

Most have actually only been TF'd to 2⁵⁶. Getting them all to 2⁶⁰ is a task which will take months, if not years, to complete.

2⁵⁶ and 2⁶⁰ respectively (if I decode it well)

Jacob

[ATH]

Originally Posted by cheesehead

Note that TF up to 2^60 on an exponent around 999,000,000 is roughly a thousand times as fast than a TF to 2^60 on an exponent around 999,000. Why? Because the potential divisors are about a thousand times as far apart for the former than for the latter, as one can deduce from the 2kn+1 requirement, so there are only one one-thousandth as many to test in the range of factor sizes up to 2^60.

Which is why it would make more sense to keep track if the bitrange of k during TF instead of bitrange of 2kn+1.