Tag: Prime number

From “The Foundations of Mathematics”
This is a fragment of a question from the first chapter of “The Foundations of Mathematics” (Amazon link): Record whether you think the following statements are true or false: (a) All of the numbers 2, 5, 17, 53, 97 are prime. (b) Each of the numbers 2, 5, 17, 53, 97 is prime. (c) Some […]

Struggling with coin tossing paradox
I was led to this by the discussion on the nonrandom nature of prime numbers – as apparently it inspired one of the authors of the paper that noted this. I am struggling a bit with the maths of this, so hopefully writing it out might either help me grasp what is wrong with my […]

Yitang Zhang latest…
A few weeks ago the world of maths was pleasantly shocked when a hitherto largely unnoticed mathematician, Yitang Zhang, demonstrated that there are infinitely many (pairs of primes) primes at most 70,000,000 apart – ie find a prime, any prime, no matter how large, and there is another two at most 70,000,000 numbers away. Zhang’s […]

“Enter any 12 digit prime to continue”
Great short blog here from John D. Cook in which he – and a commenter – show it is not such a difficult task after all – if you are clever enough to enter an odd number that doesn’t end in 5 then you have an approximately 9% chance of moving ahead.

How I discovered the fundamental theorem of arithmetic by chance
Actually, of course, I rediscovered it. I have been attempting to read, for the third time Douglas Hofstadter‘s celebrated Godel, Escher, Bach: I bought a copy in Washington DC in 2009 and loved it (though didn’t get very far before I put it down for some reason) but I have always struggled to get deeply […]

Finding “new” primes
To accompany How to Solve it, I also bought How to Prove It: A Structured Approach which deals with the construction of proofs. I am puzzled, though, by its treatment of Euclid’s famous proof of the infinite order of the set of primes. Not because it gets the proof wrong – but because I do […]

The Erdős–Straus conjecture
I came across this as a result of links to stories about Hilbert’s tenth problem, and it looks fun, so I thought I’d write a little about it. The Erdős–Straus conjecture is that for any integer then where , , and are positive integers. This is equivalent to a diophantine equation: Which is, apparently, trivially […]