Base-dependent integer sequences | Classes of prime numbers

Minimal prime (recreational mathematics)

In recreational number theory, a minimal prime is a prime number for which there is no shorter subsequence of its digits in a given base that form a prime. In base 10 there are exactly 26 minimal primes: 2, 3, 5, 7, 11, 19, 41, 61, 89, 409, 449, 499, 881, 991, 6469, 6949, 9001, 9049, 9649, 9949, 60649, 666649, 946669, 60000049, 66000049, 66600049 (sequence in the OEIS). For example, 409 is a minimal prime because there is no prime among the shorter subsequences of the digits: 4, 0, 9, 40, 49, 09. The subsequence does not have to consist of consecutive digits, so 109 is not a minimal prime (because 19 is prime). But it does have to be in the same order; so, for example, 991 is still a minimal prime even though a subset of the digits can form the shorter prime 19 by changing the order. Similarly, there are exactly 32 composite numbers which have no shorter composite subsequence: 4, 6, 8, 9, 10, 12, 15, 20, 21, 22, 25, 27, 30, 32, 33, 35, 50, 51, 52, 55, 57, 70, 72, 75, 77, 111, 117, 171, 371, 711, 713, 731 (sequence in the OEIS). There are 146 primes congruent to 1 mod 4 which have no shorter prime congruent to 1 mod 4 subsequence: 5, 13, 17, 29, 37, 41, 61, 73, 89, 97, 101, 109, 149, 181, 233, 277, 281, 349, 409, 433, 449, 677, 701, 709, 769, 821, 877, 881, 1669, 2221, 3001, 3121, 3169, 3221, 3301, 3833, 4969, 4993, 6469, 6833, 6949, 7121, 7477, 7949, 9001, 9049, 9221, 9649, 9833, 9901, 9949, ... (sequence in the OEIS) There are 113 primes congruent to 3 mod 4 which have no shorter prime congruent to 3 mod 4 subsequence: 3, 7, 11, 19, 59, 251, 491, 499, 691, 991, 2099, 2699, 2999, 4051, 4451, 4651, 5051, 5651, 5851, 6299, 6451, 6551, 6899, 8291, 8699, 8951, 8999, 9551, 9851, ... (sequence in the OEIS) (Wikipedia).

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Maximum and Minimum

Maximum and Minimum of a set In this video, I define the maximum and minimum of a set, and show that they don't always exist. Enjoy! Check out my Real Numbers Playlist: https://www.youtube.com/playlist?list=PLJb1qAQIrmmCZggpJZvUXnUzaw7fHCtoh

From playlist Real Numbers

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Discrete Math - 4.3.1 Prime Numbers and Their Properties

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From playlist Discrete Math I (Entire Course)

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This video explains some interesting facts about the last digits of prime numbers.

From playlist Mathematics General Interest

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In this video I talk about why all mathematicians are actually minimalist, to some extent. Thoughts? Opinions? Leave a comment below:)

From playlist Cool Math Stuff

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Infinite Limits With Equal Exponents (Calculus)

#Calculus #Math #Engineering #tiktok #NicholasGKK #shorts

From playlist Calculus

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In this video, we discuss how to find the absolute maximum and minimum values of a function on a closed interval.

From playlist Calculus

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solving a quadratic congruence but the modulus is NOT prime

Learn how to solve a quadratic congruence with a nonprime modulus. This is a fun math topic in number theory or discrete math! Check out an example if the module is prime: 👉https://youtu.be/cdnxOzTZRRY Subscribe for more math for fun videos 👉 https://bit.ly/3o2fMNo 💪 Support this chan

From playlist Number Theory | math for fun

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Mark Burstein - The Literary Englishman & the "Scientific American" - G4G14 Apr 2022

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Ezra (Bud) Brown - Puzzles & Wonders from Elwyn, Richard, John, Ron, and Martin - CoM Oct 2020

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Non-Linear Estimation

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Stéphane Mallat: "Deep Generative Networks as Inverse Problems"

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Introduction to prime numbers for GCSE 9-1 maths!

From playlist Prime Numbers, HCF and LCM - GCSE 9-1 Maths

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Related pages

Prime number | Composite number | Journal of Recreational Mathematics | Subsequence | Recreational mathematics | Number theory