Cryptocurrency Q&A
Why is 1 no longer prime?
Why is 1 no longer prime?
CryptoVanguard
Wed Sep 18 2024
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7 answers
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I'm intrigued by the statement that 1 is no longer considered a prime number. Could you please elaborate on the reasoning behind this change? What mathematical properties or definitions have shifted to exclude 1 from the category of prime numbers? And how does this revision impact our understanding of number theory and cryptography, which often rely on prime numbers for their security?
7 answers
IncheonBeautyBloomingRadianceGlow
Fri Sep 20 2024
The concept of prime factorization is fundamental in understanding the structure of numbers. It states that every integer greater than 1 can be expressed as a unique product of prime numbers.
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Gianluca
Fri Sep 20 2024
When we consider the factorization of a number, it becomes clear why we exclude 1 from being classified as a prime number. For instance, the number 6 can be expressed as 2 times 3, which are both prime numbers.
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CryptoPioneer
Fri Sep 20 2024
However, if we were to include 1 as a prime, then the factorization of 6 would become 2 times 3 times 1 times 1 times 1, and so on, leading to an infinite product of 1s.
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Giulia
Thu Sep 19 2024
This infinite product would contradict the uniqueness of the prime factorization theorem, which states that every number has a unique product of prime numbers.
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Dreamchaser
Thu Sep 19 2024
Therefore, it is more logical to exclude 1 from the category of prime numbers to maintain the integrity of the prime factorization theorem.
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