Is there an absolute constant C such that for every sufficiently large X one can choose primes p_i<X with ∑_i1/p_i<C and residue classes a_i pmodp_i whose union contains every integer below X?

Erdős Problem #1200 — Bounded reciprocal mass covering finite intervals

About 46 years old · traced to 1980

Is there an absolute constant $C$ such that for every sufficiently large $X$ one can choose primes $p_i<X$ with $\sum_i1/p_i<C$ and residue classes $a_i\pmod{p_i}$ whose union contains every integer below $X$ ?

References

Primary source

P. Erdős, A survey of problems in combinatorial number theory, Annals of Discrete Mathematics 6 (1980), 89–115.

Additional references

P. Erdős, A survey of problems in combinatorial number theory, Annals of Discrete Mathematics 6 (1980), 89–115.

number-theory prime-numbers

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