Category Archives: Number Theory

Q: What is the Riemann Hypothesis? Why is it so important?

Physicist: To non-mathematicians this seems like a whole lot of fuss over nothing. There’s a function called the Riemann Zeta function, denoted ““, that’s defined for complex numbers (that is, you can plug in for example, and it’s totally fine).  … Continue reading

Posted in -- By the Physicist, Equations, Math, Number Theory | 12 Comments

Q: How can quantum computers break encryption?

Physicist: What follows is the famous Shor algorithm, which can break any RSA encryption key. The problem: RSA, the most common form of public key encryption, is based on the fact that large numbers are hard to factor.  Without going … Continue reading

Posted in -- By the Physicist, Computer Science, Equations, Math, Number Theory, Physics, Probability, Quantum Theory | 19 Comments

Q: Why is it that (if you exclude 2 & 3) the difference between the squares of any two prime numbers is divisible by 12?

Physicist:  That’s a really cool property! Every prime number (other than 2 and 3) can be written in the form 6j+1 or 6j+5.  For example, 17 = 6(2)+5 and 31 = 6(5)+1. This is because numbers of the form 6j, … Continue reading

Posted in -- By the Physicist, Brain Teaser, Math, Number Theory | 8 Comments

Q: How do “Numerology Math Tricks” work? (adding digits and tricks with nines)

The original question was: Please help me solve this math card trick, I do not understand how it works: If you take a deck of 52 cards and split it into any number of piles (lets say 3) and count … Continue reading

Posted in -- By the Physicist, Brain Teaser, Math, Number Theory | 10 Comments

Q: How hard would it be to make a list of products of primes that could beat public key encryption?

The complete question was: I’m assuming almost anyone with sufficient computing power could generate big prime numbers (if these are not already published somewhere). Would making a table of all of the products of these prime numbers be so difficult? … Continue reading

Posted in -- By the Mathematician, Math, Number Theory | 1 Comment

Q: Why is the number 1 not considered a prime number?

Mathematician: Note that when we say that a number is “prime”, all that we are doing is applying a definition that was devised by mathematicians. A prime number is generally defined to be any positive number that has exactly two … Continue reading

Posted in -- By the Mathematician, Math, Number Theory | 39 Comments