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Prime Numbers
YGK These Statements About Prime Numbers
| Question | Answer |
|---|---|
| The principle that every integer >1 has a unique prime factorization | Fundamental theorem of arithmetic |
| The theorem stating there are infinitely many prime numbers | Euclid’s theorem |
| Theorem stating \(a^{p}\equiv a\quad (\mod p)\) for prime \(p\) | Fermat’s little theorem |
| Composite numbers that function as "false positives" for Fermat’s little theorem | Carmichael numbers |
| The generalization of Fermat’s little theorem for composite numbers | Euler’s theorem |
| Theorem stating \((p-1)!\equiv -1\quad (\mod p)\) if and only if \(p\) is prime | Wilson’s theorem |
| Theorem linking even perfect numbers to Mersenne primes | Euclid–Euler theorem |
| A prime number of the form \(2^{p}-1\) | Mersenne prime |
| Theorem stating \(\pi (n)\) is approximately \(n/\ln n\) | Prime number theorem |
| Cryptosystem based on the difficulty of factoring large prime products | RSA algorithm |
| Primes of the form \(2p+1\), where \(p\) is also prime | Safe primes |
| Mathematician who first studied primes of the form \(2p+1\) | Sophie Germain |
| Claim that every even integer > 2 is the sum of two primes | Strong Goldbach conjecture |
| Claim that every odd integer > 5 is the sum of three primes | Weak Goldbach conjecture |
| Mathematician who proved the weak Goldbach conjecture in 2013 | Harald Helfgott |
| Claim that all non-trivial zeros of the zeta function have real part 1/2 | Riemann hypothesis |
| Author of “On the Number of Primes Less Than a Given Magnitude” | Bernhard Riemann |
| Claim that there are infinitely many pairs of primes with a gap of 2 | Twin prime conjecture |
| Mathematician who first proved a finite bound on infinitely occurring prime gaps | Yitang Zhang |
Created by:
ahumanbeing
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