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Largest Prime Number Found: 17,425,170 Digits Long
- Context: Undergrad
- Thread starter Astronuc
- Start date
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- Prime
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Discussion Overview
The thread discusses the discovery of the largest known prime number, which is 17,425,170 digits long. Participants explore the implications of this discovery, the nature of prime numbers, and the philosophical considerations surrounding the concept of "largest" primes.
Discussion Character
- Debate/contested
- Conceptual clarification
Main Points Raised
- One participant notes that the new prime number is 2 raised to the 57,885,161 power minus 1, discovered by Curtis Cooper.
- Another participant emphasizes that it is the largest known prime number, suggesting a distinction between "largest" and "known."
- Some participants humorously propose that "infinity - 1" could be considered the largest prime, raising a philosophical question about the nature of infinity.
- A reference is made to the work of Appel & Haken regarding the burden of proof on the algorithm used to find the prime.
- One participant cites Euclid's proof that there are infinitely many primes, arguing that there cannot be a largest prime.
Areas of Agreement / Disagreement
Participants express differing views on the concept of the largest prime number, with some agreeing on the definition of "largest known" while others challenge the notion by referencing infinity and philosophical implications. The discussion remains unresolved regarding the implications of infinity in relation to prime numbers.
Contextual Notes
Participants do not fully resolve the implications of their statements about the nature of primes and infinity, leaving open questions about definitions and the philosophical aspects of prime numbers.