# Tagged Questions

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1answer
116 views

### A curious statement in an old blog

In http://blog.computationalcomplexity.org/2009/08/finding-primes.html, a statement is added which reads "Oddly enough we would usually prefer a probabilistic over the deterministic method to find ...
0answers
120 views

### Implications of a deterministic polytime prime-finding algorithm

I'm wondering what are the current known uses/implications of a polynomial-time algorithm for the following problem: Given $n$ in binary, output a prime $p > n$. I'm both curious about ...
2answers
415 views

### Why does most cryptography depend on large prime number pairs, as opposed to other problems?

Most current cryptography methods depend on the difficulty of factoring numbers that are the product of two large prime numbers. As I understand it, that is difficult only as long as the method used ...
2answers
301 views

### Does “Productive function” mean just that in ME O'Neill, The Genuine Sieve of Eratosthenes?

M.E. O'Neill in the Epilogue of "The Genuine Sieve of Eratosthenes" (preprint http://www.cs.hmc.edu/~oneill/papers/Sieve-JFP.pdf DOI 10.1017/S0956796808007004) quotes Richard Bird that "union is ...
2answers
690 views

### What's the most efficient algorithm for Divisibility?

What is the most efficient (in time complexity) algorithm known nowadays for the Divisibity Decision Problem: given two integers, say $a$ and $b$, does $a$ divide $b$? Let it be clear that what I ask ...
3answers
4k views

### Why can machine learning not recognize prime numbers?

Say we have a vector representation of any integer of magnitude n, V_n This vector is the input to a machine learning algorithm. First question : For what type of representations is it possible to ...
2answers
353 views

### What are TCS conjectures that were proved for primes and small values but then turned out to be false?

Are there any conjectures in theoretical computer science that involve some parameter n and were proved for small values of n AND for primes but later turned out to be false? In number theory such ...
1answer
327 views

### Computational complexities in factoring

[Note: n is a given integer (not the number of its digits)] I'd like to know how O(sqrt(n)/log(n)) would compare against the computational complexity of the best available algorithms (as well as the ...
1answer
704 views

### Does Conway's PRIMEGAME generate all prime powers of 2?

Most sites I have visited reading on this interesting topic state something along the lines "the only powers of two (other than 2 itself) that occur in this sequence are those with prime exponent" ...
0answers
155 views

### Complexity of computing logarithm of a prime power

Suppose $n = p^k$ for some prime number $p$ and some non-negative integer $k$. What is (the best-known upper bound on) the complexity of computing $k$ on input $n$ (given in binary)? It is important ...
1answer
76 views

### Rabins Signature Implementation [closed]

I am searching for an Implementation for Rabins Algorithm in any language. I've searched but haven't got it anywhere. does anybody have a link ?
2answers
2k views

### Are the problems PRIMES, FACTORING known to be P-hard?

Let PRIMES (a.k.a. primality testing) be the problem: Given a natural number $n$, is $n$ a prime number? Let FACTORING be the problem: Given natural numbers $n$, $m$ with $1 \leq m \leq n$,...
2answers
269 views

### How to calculate the cost of factoring a large integer?

I would like to know how much it would cost to factor a large integer. The cost can be given computer operations, time to process it or even monetary value. I know there are people that factored 200 ...
0answers
254 views

### Conditional density of primes

We have some theorems about the density of prime numbers, the most famous one is probably the prime number theorem. My question is about the density of primes when we choose random numbers from ...
2answers
890 views

### Finding a prime greater than a given bound

Is a deterministic polynomial-time algorithm known for the following problem: Input: a natural number $n$ (in binary encoding) Output: a prime number $p > n$. (According to a list of open ...