All Questions
Tagged with nt.number-theory prime-numbers
1,808 questions
12
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Covering the primes by 3-term APs ?
Hello, the Green-Tao theorem says infinitely many k-term Arithmetic Progressions exist for any integer k.
My question is: can we actually partition the primes into 3-term APs only (or is there a ...
- 2,901
7
votes
2
answers
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Density of a subset of the reals
The rationals are clearly dense in the real number system, i.e. for every pair a < b of real numbers there exists a rational number p/q s.t. a < p/q < b. I conjecture the same to be true with ...
- 2,479
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7
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What is the smallest integer whose primality status is not known? [closed]
Closely related: what is the smallest known composite which has not been factored? If these numbers cannot be specified, knowing their approximate size would be interesting. E.g. can current ...
- 299
9
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6
answers
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Primes are pseudorandom?
I've been reading the wonderful slides by Terry Tao and thought about this question.
Primes appear to be quite random, and the formal statement should be that there are some characteristics of primes ...
- 15.1k
9
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1
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The large sieve for primes
Let $\Lambda(n)$ be the von Mangoldt function, i.e., $\Lambda(n) = \log p$ for $n$ a prime power $p^k$ and $\Lambda(n) = 0$ for all $n$ that not prime powers. Let
$$S(\alpha) = \sum_{n \leq N} \...
- 20.2k
13
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6
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Applications and Natural Occurrences of Prime Numbers
I'm fascinated by prime numbers, and over the years, I've found multiple applications and natural occurrences for them. But can anyone suggest some alternatives that aren't in my list?
Applications ...
15
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6
answers
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Why the search for ever larger primes?
I understand why primes are useful numbers and also why the product of large primes are useful such as for application in public key cryptography, but I am wondering why it is useful to continue the ...
- 261
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4
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Arithmetic progressions without small primes
The following question came up in the discussion at How small can a group with an n-dimensional irreducible complex representation be? :
Is it known that there are infinitely many primes p for which ...
- 156k