We publish our first data on the Collatz function for 2^{37156667} – 1 (#7 known megaprime) and two of its odd neighbors located at ±26.

# Category Archives: Main

# Collatz function data for 2^32582657 – 1 (#8 known megaprime)

We publish our first data on the Collatz function for 2^{32582657} – 1 (#8 known megaprime) and two of its odd neighbors located at ±71149323674102624414.

# Collatz function data for 10223×2^31172165 + 1 (#9 known megaprime)

We publish our first data on the Collatz function for 10223×2^{31172165} + 1 (#9 known megaprime) and two of its odd neighbors located at ±4.

# Collatz function data for 2^30402457 – 1 (#10 known megaprime)

We publish our first data on the Collatz function for 2^{30402457} – 1 (#10 known megaprime) and two of its odd neighbors located at ±2.

# 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

# 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 10^{16} become possible in reasonable time without supercomputers and massively parallel processing (MPP).