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 Check out the coolest math clothes in the world: https://mathshion.com/ Join Wrath of Math to get exclusive videos, lecture notes, and more: https://www.youtube.com/channel/UCyEKvaxi8mt9FMc62MHcliw/join More Math Chats: https://www.youtube.com/playlist?list=PLztBpqftvzxXQDmPmSOwXSU9vOHgty1RO Outro music: https://youtube.com/shorts/tfifiSdTZRg Follow Wrath of Math on... ● Instagram: https://www.instagram.com/wrathofmathedu ● TikTok: https://www.tiktok.com/@wrathofmathedu ● X: https://x.com/wrathofmathedu 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