Usually, it is quite easy (if cumbersome) to translate a formula like "if $\varepsilon$ is infinitesimal, and if $f$ is differentiable at $a$, $f'(a)$ is the shadow of $\frac{f(a+\varepsilon)-f(a)}{\varepsilon}$". But I cannot find a standard translation of the conjecture :"There exists a galaxy of non-standard integers containing an infinite number of primes", where galaxies are the equivalence classes of $\mathbb N$ by the relation $m\simeq n \iff (m-n)$ is standard. The closest I can find is the k-tuple conjecture (the first of the Hardy-Littlewood conjectures), but it seems obvious this is quite stronger than mine.



Translation of a non-standard analysis formulation
How about this ...


Let's say a finite set $V \subseteq \mathbb N$ is a **Feldmann set** iff there are infinitely many $n$ such that for all $u \in V$, $n+u$ is prime. 


For example, $\{0,2\}$ is a Feldmann set iff there are infinitely many twin primes.


Your equivalent statment: there are arbitrarily large Feldmann sets.


