### (testing signal)

A consensus algorithm is a process in computer science used to achieve agreement on a single data value among distributed processes or systems. Consensus algorithms are designed to achieve reliability in a network involving multiple unreliable nodes. As a result, consensus algorithms must be fault-tolerant. Lets review some of the most popular algos:

PROOF OF WORK (PoW)
A proof of work is a piece of data which is difficult (costly, time-consuming) to produce but easy for others to verify and which satisfies certain requirements. Producing a proof of work can be a random process with low probability so that a lot of trial and error is required on average before a valid proof of work is generated.

Bitcoin uses the Hashcash proof of work system.… Read more...

The subtitle of Matthew Bothwell’s wrap-up on ‘Oumuamua is most informative: An alien-made artefact or just interstellar debris? What ʻOumuamua says about how science works when data is scarce.

At least one astronomer, Harvard’s Avi Loeb, insisted that ‘Oumuamua must be an “extraterrestrial light sail.” And few suggested that that couldn’t possibly be true.

Right. What do we do when we are not sure? Bothwell, author of the forthcoming Invisible Universe, offers some thoughts. W all imagine ET in our own image:

Victorians of the late 19th century, living in the era of ambitious engineering, looked at Mars and saw globe-spanning canals – evidence, they believed, of a grand industrial civilisation mirroring their own.

This article focuses on the machine learning aspects of the problem, and the use of pattern recognition techniques leading to interesting, new findings about twin primes. Twin primes are prime numbers p such that p + 2 is also prime. For instance, 3 and 5, or 29 and 31. A famous, unsolved and old mathematical conjecture states that there are infinitely many such primes, but a proof still remains elusive to this day. Twin primes are far rarer than primes: there are infinitely more primes than there are twin primes, in the same way that that there are infinitely more integers than there are prime integers.

Here I discuss the results of my experimental math research, based on big data, algorithms, machine learning, and pattern discovery.

In case you’ve missed it, there has been a tremendous number of news stories, social media posts and the like on Bitcoin, Hashing Algorithms, Blockchain, video graphics cards and Crypto-mining.  If you are anything like the most of us, the information barely provides you a platform to have a discussion about the topic.  But what does it all mean?  What is a Blockchain?  What are hashing algorithms?  How does one mine for bitcoins or any other crypto-currencies?  Is it as profitable as most say?  These and many other questions will be addressed in this blog.

PrimeNet – For the past few years, I’ve really been intrigued with the application of prime numbers in public key encryption algorithms.  As a result, I decided to join a community of mathematicians in search of the largest prime number.

A curious pattern, approximations for pi, and prime distributions.
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Based on this Math Stack Exchange post:
https://math.stackexchange.com/questions/885879/meaning-of-rays-in-polar-plot-of-prime-numbers/885894

Also, if you haven’t heard of Ulam Spirals, you may enjoy this Numberphile video:

Dirichlet’s paper:
https://arxiv.org/pdf/0808.1408.pdf

Important error correction: In the video, I say that Dirichlet showed that the primes are equally distributed among allowable residue classes, but this is not historically accurate.… Read more...

an indivisible gang generated with Python in 0.07s

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997

import time
start = time.time()