BIM-MPS_Reference

References

REFERENCES: Primes

While there are no specific references for this work other than referring back to my own original work, there are many references involved in the study and research on the PRIMES in general. These have been well documented in the TPISC_IV: Details_BIM+PPT+PRIMES focus white paper. This paper also contains the background graphics and tables leading up to this current work. The focus page is part of the much larger TPISC_IV: Details ebook project that is freely available as an HTML webpage. The quick reference outline can be found here. An overall INDEX can be found here.

REFERENCES: Mersenne Primes, Perfect Numbers

Scroll down for Internal Reference Links

Some Basic References and Resources http://5010.mathed.usu.edu/Fall2018/NWestfall/ref_res.html

A000043 - OEIS_MersennePrime-n_values.pdf https://oeis.org/A000043

A000396 - OEIS_PerfectNumbers.pdf https://oeis.org/A000396

Elliptic curve primality certificates.pdf https://www.johndcook.com/blog/2023/01/13/ecpp/

Euclid–Euler theorem - Wikipedia.pdf https://en.wikipedia.org/wiki/Euclid–Euler_theorem

Even_Perfect_Numbers_and_Their_Eulers_Function.pdf https://www.researchgate.net/publication/26534995_Even_Perfect_Numbers_and_Their_Euler's_Function

Great Internet Mersenne Prime Search - PrimeNet.pdf https://www.mersenne.org

List of known Mersenne prime numbers - PrimeNet.pdf https://www.mersenne.org/primes/

List of known Mersenne primes - Prime-Wiki.pdf https://en.wikipedia.org/wiki/List_of_Mersenne_primes_and_perfect_numbers

List of perfect numbers - Wikipedia.pdf https://en.wikipedia.org/wiki/Perfect_number, https://handwiki.org/wiki/List_of_perfect_numbers

List_of_Mersenne_primes_and_perfect_numbers.pdf https://en.wikipedia.org/wiki/List_of_Mersenne_primes_and_perfect_numbers

LondonToll_prime-tutorial.pdf http://www.isthe.com/chongo/tech/math/prime/mersenne.html , http://www.isthe.com/chongo/tech/math/prime/prime-tutorial.pdf

MathleteNation_DavidKramer+Hex#.rtfd http://mathletenation.com/node

Mersenne Number -- from Wolfram MathWorld.pdf https://mathworld.wolfram.com/MersenneNumber.html

Mersenne prime - Wikipedia.pdf https://en.wikipedia.org/wiki/Mersenne_prime

Mersenne Prime -- from Wolfram MathWorld.pdf https://mathworld.wolfram.com/MersennePrime.html

Mersenne prime digits.pdf http://www.isthe.com/chongo/tech/math/prime/mersenne.html

Mersenne primes - Rosetta Code.pdf https://rosettacode.org/wiki/Mersenne_primes

Mersenne Primes using Lucas Lehmer Primality Test in Python | by Himanshu Sharma | Medium.pdf https://medium.com/@cehimanshusharma94/mersenne-primes-using-lucas-lehmer-primality-test-in-python-80b2ca792911

Mersenne Primes. Number Mysteries and the Hunt for Large… | by Kasper Müller | Cantor’s Paradise | J.pdf https://www.cantorsparadise.com/mersenne-primes-374d9d25fd8e

Mersenne Primes/ History, Theorems and Lists.pdf https://t5k.org/mersenne/#known

Perfect number - Wikipedia.pdf https://en.wikipedia.org/wiki/Perfect_number

perfect number | Definition & Facts | Britannica.pdf https://www.britannica.com/science/Mersenne-prime

Perfect Numbers. An ancient riddle | by Kasper Müller | Cantor’s Paradise | Feb, 2021 | Medium.pdf https://www.cantorsparadise.com/perfect-numbers-db0b0c15c21a

Perfect_number.pdf https://mathshistory.st-andrews.ac.uk/HistTopics/Perfect_numbers/

perfelct_numbers-051015.pdf https://math.dartmouth.edu/~jvoight/notes/perfelem-051015.pdf

Pratt Primality Certificates.pdf https://www.johndcook.com/blog/2023/01/03/pratt-certificate/ , https://mathworld.wolfram.com/PrattCertificate.html , https://mathworld.wolfram.com/PrattCertificate.html

Python Exercise/ Check whether a number is perfect or not - w3resource.webarchive https://www.w3resource.com/python-exercises/python-functions-exercise-11.php

Quanta Magazine.pdf https://www.quantamagazine.org/tag/prime-numbers , https://www.quantamagazine.org/the-mysterious-math-of-perfect-numbers-20210315/

Special primality proofs.pdf https://cs.indstate.edu/Summer/summer.pdf , https://en.wikipedia.org/wiki/Wilson%27s_theorem , https://www.johndcook.com/blog/2023/01/17/special-primality-proofs/

Square number - Wikipedia.pdf https://en.wikipedia.org/wiki/Square_number

Square-free integer - Wikipedia.pdf https://en.wikipedia.org/wiki/Square-free_integer

StalkingTheRiemannHypothesis.rtf https://www.maa.org/press/maa-reviews/stalking-the-riemann-hypothesis-the-quest-to-find-the-hidden-law-of-prime-numbers

largest-prime-number-has-23249425-digits.pdf https://t5k.org , https://t5k.org/mersenne/

TotDEuclidEuler.pdf https://www.theoremoftheday.org/NumberTheory/EuclidEuler/TotDEuclidEuler.pdf

NEXT: Appendix I: Cubed, Coordinates

LINKS:

Mersenne Prime Squares (Part I) the Introductory white paper.

Mersenne Prime Squares (Part II) 3 Simple Intros.

Mersenne Prime Squares (Part III) the Advanced white paper.

The MPS Project The Mersenne Prime Squares Project.

LINKS:

MathspeedST: TPISC Media Center

MathspeedST: eBook (free)

Apple Books

Artist Link in iTunes Apple Books Store: Reginald Brooks

Back to Part I of the BIM-Goldbach_Conjecture.

Back to Part III of the BIM-Goldbach_Conjecture.

BACK: ---> PRIMES Index on a separate White Paper

BACK: ---> Periodic Table Of PRIMES (PTOP) and the Goldbach Conjecture on a separate White Paper (REFERENCES found here.)

BACK: ---> Periodic Table Of PRIMES (PTOP) - Goldbach Conjecture ebook on a separate White Paper

BACK: ---> Simple Path BIM to PRIMES on a separate White Paper

BACK: ---> PRIMES vs NO-PRIMES on a separate White Paper

BACK: ---> TPISC_IV: Details_BIM+PTs+PRIMES on a separate White Paper

BACK: ---> PRIME GAPS on a separate White Paper

Reginald Brooks

Brooks Design

Portland, OR

brooksdesign-ps.net

KEYWORDS TAGS: BMP, BIM-MersenneSquare-PerfectNumber, Mersenne Primes, Mersenne Prime Square, Perfect Number, Perfect Square, MPS, Mp, PTOP, Periodic Table Of PRIMES, PRIMES vs NO-PRIMES, algebraic geometry, BIM, TPISC, The Pythagorean - Inverse Square Connections, Pythagorean Triangles, DNA, Zika virus, pentagon, decagon, double pentagon, composite axial DNA double-helix, Pythagorean Triples, primitive Pythagorean Triples, non-primitive Pythagorean Triples, Pythagorean Theorem, Pythagorus Theorem, The Dickson Method, BBS-ISL Matrix, Expanded Dickson Method, r-sets, s-set, t-sets, Pair-sets, geometric proofs, MathspeedST, leapfrogging LightspeedST FASTER than the speed of light, Brooks (Base) Square- Inverse Square Law (ISL), BBS-ISL Matrix grid, The Architecture Of SpaceTime (TAOST), The Conspicuous Absence Of Primes (TCAOP), A Fresh Piece Of Pi(e), AFPOP, Numbers of Inevitability, LightspeedST, Teachers, Educators and Students (TES), number theory, ubiquitous information, FASTER than the speed of light, primes, prime numbers, fractals, mathematics, Universe, cosmos, patterns in number, DSEQEC, Double-Slit Experiment-Quantum Entanglement Conjecture, CaCost, Creation and Conservation of SpaceTime.

Art Theory 101 / White Papers Index

PIN: Pattern in Number...from primes to DNA. | PIN: Butterfly Primes...let the beauty seep in. | PIN: Butterfly Prime Directive...metamorphosis. | PIN: Butterfly Prime Determinant Number Array (DNA) ~conspicuous abstinence~. | GoDNA: the Geometry of DNA (axial view) revealed. | SCoDNA: the Structure and Chemistry of DNA (axial view). | The LUFE Matrix | The LUFE Matrix Supplement | The LUFE Matrix: Infinite Dimensions | The LUFE Matrix: E=mc² | Dark Matter=Dark Energy | The History of the Universe in Scalar Graphics | The History of the Universe_update: The Big Void | Quantum Gravity ...by the book | The Conservation of SpaceTime | LUFE: The Layman's Unified Field Expose` | GoMAS: The Geometry of Music, Art and Structure ...linking science, art and esthetics. Part I | Brooks (Base) Square (BBS): The Architecture of Space-Time (TAOST) and The Conspicuous Absence of Primes (TCAOP) - a brief introduction to the series | more White Papers...

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