# Tagged Questions

**1**

vote

**2**answers

238 views

### Infinite play with tape, or covering the integers with prime arithmetic progressions

It is possible that a more technical version of this question has been
asked and answered in the literature. If so, then a reference is much
appreciated. I will phrase it in terms of colored tapes ...

**14**

votes

**2**answers

502 views

### Unboundedness of primes in bounded arithmetic

Wilkie's well known question asks whether $I\Delta_{0}$ proves the unboundedness of primes. We know that by adding a sentence to $I\Delta_{0}$ which says "the exponential function is total", it is ...

**3**

votes

**1**answer

416 views

### Forcing and divisibility

A version of this question got a couple of comments but no answer on stackexchange.
I learned the concept of forcing in logic from Boolos & Jeffrey's book Computability and Logic (second edition, ...

**7**

votes

**1**answer

412 views

### Is there a two-variable prime-representing polynomial (in the sense of Jones-Sato-Wada-Wiens)?

In the math.se question Proof of no prime-representing polynomial in 2 variables, Alon Amit asks if Ribenboim's claim that a prime-representing polynomial (a Diophantine polynomial in which the ...

**9**

votes

**2**answers

849 views

### Non-Standard Prime

Hello,
My question is about the non-standard models of the integers. If we add to the Peano's axioms $P$ of arithmetic the following axioms for a fixed constant $c$:
$c \neq 0$, $c \neq 1$, $c \neq ...

**19**

votes

**1**answer

1k views

### Nontrivial circular arguments?

There is a famous circular argument for the Prime Number Theorem (PNT). It turns
out that there exists an infinite sequence of elementary-to-prove Chebyshev-type estimates
that taken together imply ...

**4**

votes

**1**answer

425 views

### Implication of Polignac's conjecture on prime distribution in models of PA

Polignac's conjecture (PC) is that there exists infinitely many pairs of consecutive prime numbers that are a distance $d$ apart for some natural number $d$. The twin prime conjecture is the ...

**24**

votes

**3**answers

2k views

### Composite pairs of the form n!-1 and n!+1

It's well known that the numbers of the form $n!\pm1$ are not always prime. Indeed, Wilson's Theorem guarantees that $(p-2)!-1$ and $(p-1)!+1$ are composite for every prime number $p > 5$.
Is ...

**5**

votes

**1**answer

929 views

### Polynomial representing prime numbers

Along the lines of Polynomial representing all nonnegative integers, but likely well-known question:
is there a polynomial $f \in \mathbb Q[x_1, \dots, x_n]$ such that $f(\mathbb Z\times\mathbb ...