Discover the Massive 5,382-Digit Prime Number in the USA 🇺🇸

The United States of America prime is a 5,382 digit prime number found by Vadim Ponomarenko and tested using the Baillie–PSW primality test. The number passed the test, making it highly likely to be a prime number that looks like the American flag, but later Robert Baillie himself verified the number is prime using Pari/GP. Today we discuss the Baillie-PSW primality test you could use yourself to find a prime number that looks like your country's flag, and discuss several necessary concepts involved including Fermat primes, Fermat's Little theorem, the strong probably prime test, the Jacobi Symbol, the Legendre Symbol, and Lucas sequences. Happy Independence Day. #maths #mathematics

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SOURCES
Ponomarenko, Vadim. “The United States of America Prime.” Math Horizons, vol. 28, no. 4, 2021, p. 19. JSTOR, https://www.jstor.org/stable/48665195.
Prime Numbers: A Computational Perspective by Carl Pomerance and Richard Crandall
Pomerance, Carl, et al. “The Pseudoprimes to $25 \cdot 10^9$.” Mathematics of Computation, vol. 35, no. 151, 1980, pp. 1003–26. JSTOR, https://doi.org/10.2307/2006210.
https://math.umd.edu/~immortal/MATH406/lecturenotes/ch11-3.pdf
SOME COMMENTS ON BAILLIE-PSW PSEUDOPRIMES by Chen and Greene
https://cs.stackexchange.com/questions/69386/more-details-about-the-baillie-psw-test/77811#77811
https://en.wikipedia.org/wiki/Baillie%E2%80%93PSW_primality_test#The_test
https://www.mathworks.com/help/symbolic/jacobisymbol.html
https://github.com/sagemath/sage/blob/develop/src/sage/arith/misc.py#L575
https://mathworld.wolfram.com/Baillie-PSWPrimalityTest.html

0:00 Intro
1:43 Checking Primes
3:10 The USA Prime
4:34 Fermat's Little Theorem
9:01 Base 2 Strong Probable Prime Test
14:17 Step 2
16:46 Legendre Symbol
18:35 Jacobi Symbol
20:14 D, P, Q
22:15 Lucas Sequence
25:33 119 is Pseudoprime
26:44 A Really Good Test
27:55 Method
28:34 Conclusion