We publish our first data on the Collatz function for 230402457 – 1 (#10 known megaprime) and two of its odd neighbors located at ±2.
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Sequence of record 288-step delayed palindromes found
On 26 April 2019, Rob van Nobelen discovered the 23-digit number 12000700000025339936491 – the first one that takes record-breaking 288 steps to reach a final 142-digit palindrome. The previous record (261 steps) was set in 2005.
We expanded the found number to a sequence with 19353600 terms in total. This sequence currently includes all known 288-step delayed palindromes.
All results are contributed to OEIS and will be published in due course.
Collatz function data for 2^25964951 – 1 (#11 known megaprime)
We publish our first data on the Collatz function for 2^25964951 – 1 (#11 known megaprime) and two of its odd neighbors located at ±2. Continue reading
Collatz function data for 2^24036583 – 1 (#12 known megaprime)
We publish our first data on the Collatz function for 2^24036583 – 1 (#12 known megaprime) and two of its odd neighbors located at ±2. Continue reading
Collatz function data for 2^20996011 – 1 (#13 known megaprime)
We publish our first data on the Collatz function for 2^20996011 – 1 (#13 known megaprime) and two of its odd neighbors located at ±2. Continue reading
Collatz function data for 1059094^1048576 + 1 (#14 known megaprime)
We publish our first data on the Collatz function for 1059094^1048576 + 1 (#14 known megaprime) and two of its odd neighbors located at ±4. Continue reading
Collatz function data for 919444^1048576 + 1 (#15 known megaprime)
We publish our first data on the Collatz function for (919444^1048576 + 1 (#15 known megaprime) and two of its odd neighbors located at ±10. Continue reading
Collatz function data for 168451×2^19375200 + 1 (#16 known megaprime)
We publish our first data on the Collatz function for 168451×2^19375200 + 1 (#16 known megaprime) and its closest 2 odd neighbors. Continue reading
Collatz conjecture test for the Top 16 megaprimes started
We have started to test the Collatz conjecture for the Top 16 megaprimes as well as some of their selected odd neighbors. The results will be published in due course.
Breakthrough Junior Challenge 2019 Video: Chebyshev’s Bias
New 7th sign-changing zone for ∆{24;13,1}(x) in Chebyshev’s bias found
Chebyshev’s Bias: 165 Years of History
Intel ISEF 2019 Video Presentation
Switch to multi-threading for Chebyshev’s bias software
We started to develop a new version of our “4000 Chebyshev’s Bias Tester” that uses OpenMP for multi-threading.
Initial tests indicated that the test speed could be increased 4-5 times on a 4-core 8-thread processor that launches 8 copies of primesieve as a real-time prime number generator.
With the advent of affordable multi-core processors such as 32-core 64-thread AMD Ryzen™ Threadripper™ 2990WX Processor, the ranges beyond 1016 become possible in reasonable time without supercomputers and massively parallel processing (MPP).