The third video in a trilogy of Mathologer videos dealing with sum-equals-product identities and equations. The other two are: Way beyond the golden ratio The power of AB=A+B (Mathologer masterclass) Heron’s formula: What is the hidden meaning of 1 + 2 + 3 = 1 x 2 x 3 ? Today's video is all about how 2+2=2x2 and 1+2+3=1x2x3 first extends to an infinite sequence of similar identities and then further to a whole world of sum-equals-product identities. And we chase down a new connection to the so-called Sophie Germain primes. 00:00 Intro 06:27 How many? 11:29 New from old 19:53 Sophie’s primes 27:47 Beyond Sophie 30:15 Thank you!! Currently the following paper is the best introduction to the sum-equals-product problem circle of ideas: Maciej Zakarczemny, On the equal sum and product problem Very nice translation of this circle of ideas into a set of problems for the Michigan Lemma 2020 maths competition (starts with Problem 2) ~michiganlemma/material/2020/ Check out the Encyclopedia and integer sequences pages for 2,3,4,6,24,114,174,444 and 7,8,9,10,12,14,15,16,18,20,22,30 Some other papers to check out with links: Michael W. Ecker, When Does a Sum of Positive Integers Equal Their Product? M. A. Nyblom, Sophie Germain primes and the exceptional values of the equal-sum-and-product problem Maciej Zakarczemny, Equal-Sum-Product problem II M. A. Nyblom and C. D. Evans, An Algorithm to Solve the Equal-Sum-Product Problem Leo Kurlandchik and Andrzej Nowicki, When the sum equals the product :// ~anow/ps-dvi/ Combo class video on the same question Check out the list of updates in my comment that's pinned to the top of the comment section. Music: Just jump by Ian Post T-shirt: Forgot where I got this one from :( Enjoy! Burkard