First sign-changing zones for ∆{24;19,1}(x) in Chebyshev’s bias found

On December 27, 2017 our “4000 Chebyshev Bias Tester” completed testing all primes up to 10*1014  and found 5 first and previously unknown sign-changing zones for ∆{24;19,1}(x), where the value of ∆{24;19,1}(x) equals to -1. Continue reading

First sign-changing zones for ∆{24;17,1}(x) in Chebyshev’s bias found

On December 27, 2017 our “4000 Chebyshev Bias Tester” completed testing all primes up to 10*1014  and found 3 first and previously unknown sign-changing zones for ∆{24;17,1}(x), where the value of ∆{24;17,1}(x) equals to -1. Continue reading

New sign-changing zones for ∆{24;13,1}(x) in Chebyshev’s bias found

On December 20, 2017 our “4000 Chebyshev Bias Tester” completed testing all primes up to 10*1014  and found 5 new and previously unknown sign-changing zones for ∆{24;13,1}(x), where the value of ∆{24;13,1}(x) equals to -1. Continue reading

Data on first sign-changing zone for ∆{8;7,1}(x) in Chebyshev’s bias included into OEIS

As we reported before, on November 20, 2017 we submitted two our sequences for registration with OEIS. The sequences fully defined the first found sign-changing zone for ∆{8;7,1}(x) in Chebyshev’s bias. Continue reading

Number of steps in Collatz sequence for Mersenne primes from 46th to 49th published in OEIS

On November 14, 2017 our data on number of steps in Collatz sequence for Mersenne primes with the provisional index from 46th to 49th were included in OEIS as a comment to A181777. Prior to this A181777 contained information up to the 45th Mersenne prime only. Continue reading

First sign-changing zone for ∆{8;7,1}(x) in Chebyshev’s bias found

On November 10th, 2017 our “4000 Chebyshev Bias Tester” fully determined the first sign-changing zone for ∆{8;7,1}(x) in Chebyshev’s bias (where ∆{8;7,1}(x) is equal to -1).

This zone starts with the prime 192252423729713, includes 234937 terms and ends with the prime 192876135747311. Continue reading

Full data on all 8 zones with 0 values for ∆{4;3,1}(x) in Chebyshev’s bias published

Оn October 15, 2017 we published in Online Encyclopedia of Integer Sequences (OEIS) under  A007351 the full data on all 419467 primes where ∆{4;3,1}(x) is equal to zero. Staring from 27410th term equal to 9103362505753 the published sequence includes data on the 8th sign-changing zone, that was predicted back in 2001 by a group of American mathematicians, but was never actually found. Continue reading

Full data on all 8 sign-changing zones for ∆{4;3,1}(x) in Chebyshev’s bias published

On October 13, 2017 we published in Online Encyclopedia of Integer Sequences (OEIS) under  A007350 the full data on all 194367 primes where ∆{4;3,1}(x) changes sign. Staring from 12502nd term equal to 9103362505801 the published sequence includes data on the 8th sign-changing zone, that was predicted back in 2001 by a group of American mathematicians, but was never actually found. Continue reading

Full data on all 8 negative zones for ∆{4;3,1}(x) in Chebyshev’s bias published (continued)

On October 6, 2017, in addition to A051025, we published in Online Encyclopedia of Integer Sequences (OEIS) under A051024 the full data on the numbers of all 418933 primes where ∆{4;3,1}(x) becomes equal to -1. Staring from 27556th term equal to 316064952540 (that corresponds to the prime 9103362505801) the published sequence includes data on the 8th negative zone, that was predicted back in 2001 by a group of American mathematicians, but was never actually found. Continue reading

New and unknown 9th sign-changing zone in Chebyshev’s bias for ∆{4;3,1}(x) found

On October 10th, 2017 our  “4000 Chebyshev Bias Tester”  completed testing all primes up to 10*1013  and found a new and previously unknown 9th sign-changing zone for ∆{4;3,1}(x), where the value of ∆{4;3,1}(x) equals to -1. Continue reading

Full data on all 8 negative zones for ∆{4;3,1}(x) in Chebyshev’s bias published

On October 6, 2017 we published in Online Encyclopedia of Integer Sequences (OEIS) under A051025 the full data on all 418933 primes where ∆{4;3,1}(x) becomes equal to -1. Staring from 27556th term equal to 9103362505801 the published sequence includes data on the 8th negative zone, that was predicted back in 2001 by a group of American mathematicians, but was never found. Continue reading

8th sign-changing zone in Chebyshev’s bias for ∆{4;3,1}(x) found

On October 1st, 2017 our  “4000 Chebyshev Bias Tester”  completed testing all primes up to 10*1012  and found the 8th sign-changing zone for ∆{4;3,1}(x), predicted in 2001 by American mathematicians  Carter Bays, Kevin Ford, Richard H. Hudson and Michael Rubinstein to be around 9.318*1012 . Continue reading

Number of steps in Collatz sequence for Mersenne primes available for download

The data on the number of steps to reach one in Collatz sequence for Mersenne primes from the 1st to 45th (the last with confirmed index) became available for download from OEIS (A181777). The full sequence from the 1st to 49th Mersenne prime (the last known as of today) could be downloaded from our repository.

We contunue to publish our results in due course.

Number of steps in Collatz sequence for Mersenne primes published

On September 22, 2017 our data on number of steps in Collatz sequence for Mersenne primes were included in OEIS as an addition to A181777. Prior to this A181777 contained information up to the 42nd Mersenne prime only. Continue reading

Provisional 49th Mersenne prime M74207281 supports Collatz conjecture

On September 19th, 2017 our “3007 Collatz Tester for Mersenne Primes” (the improved version of “3000 Collatz Tester”) tested the provisional 49th Mersenne prime M74207281 for being in agreement with Collatz conjecture and supported it. Continue reading