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Abstract
Finding formulae for the nth prime is one of the important topics in number theory. For many years, the enthusiasm for searching for prime number formulas has remained high. In this paper, I give two expressions of the nth prime.
Two expressions of the nth prime
10 June 2026, Version 1
Working Paper
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This content is an early or alternative research output and has not been peer-reviewed by Cambridge University Press at the time of posting.
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Comment number 5, Taha Muhammad: Jun 17, 2026, 19:16
Taha Muhammad
Jun 17, 2026, 19:16
5
Taha’s Detector of Prime Number By Taha Muhammad/ USA Kurd Honorable dear prof> Tao, my work at Google Document: Link below: https://docs.google.com/document/d/1TokqbnWxWfNmx-1zW_VJxjnB9gd9O4XgYG0efG91bss/edit?usp=sharing
Comment number 4, Taha Muhammad: Jun 14, 2026, 17:10
List (1) = {} List (2) = {1} List (3) = {1,2} List (4) = {1, 2,3} List (5) = {1,2,3,4} *List (6) = {1,2,3,4,5} List (7) = {1, 2,3,4,5,6} *List (8) = {1, 2,3,4,5,6,7} List (9) = {1, 2,3,4,5,6,7,8} List (10) = {1, 2,3,4,5,6,7,8,9} List (11) = {1, 2,3,4,5,6,7,8,9,10} List (12) = {1, 2,3,4,5,6,7,8,9,10,11} List (13) = {1, 2,3,4,5,6,7,8,9,10,11,12} *List (14) = {1, 2,3,4,5,6,7,8,9,10,11,12,13} List (15) = {1, 2,3,4,5,6,7,8,9,10,11,12,13,14} List (16) = {1, 2,3,4,5,6,7,8,9,10,11,12,13,14,15} List (17) = {1, 2,3,4,5,6,7,8,9,10,11,12,13,14,15,16} List (18) = {1, 2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17} List (19) = {1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18} I told any integer has a list above! My proof of Twin Prime Conjecture (Way 3) at YouTube, Book at Amazon, Google Doc, and Cambridge Open Engage! Same my idea!!!? Author: Taha Muhammad/ USA Kurd Iraq - Independent Math Researcher. I hope Honorable Prof. Tao Tang will evaluate at least please my Collatz Golden Way...It is just one page. Can you please?
Comment number 3, Taha Muhammad: Jun 13, 2026, 09:13
https://docs.google.com/document/d/1zTT8tMJxaAjbZYFf2ZGSMDyKqjnrYpH9NRkaE4vUPt4/edit?usp=sharing By Taha Muhammad/ USA Kurd at Google Doc.
Comment number 2, Taha Muhammad: Jun 13, 2026, 09:10
https://docs.google.com/document/d/1e7ewFqv0IPOfAYeV6mM5F2C6kfm7Wqt93pLj7xbasXw/edit?usp=sharing Twin Prime by Taha Muhammad/ USA Kurd Iraq at Google Doc.
Comment number 1, Taha Muhammad: Jun 12, 2026, 02:54
Great work. My Collatz Sequence, Euler Perfect Box, Fermat's Last and General Case, Pythagorean Theorem, Roots by hand for any real #, Twin Primes, Goldbach S & W Solutions at Google Doc, C Open Engage, Book at Amazon.com., and YouTube. Taha Muhammad/ USA Kurd Iraq
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Jun 10, 2026 Version 1
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