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Statement

Conjecture (p. 90), stated after (7):

$${\sum_{p\le n}}^{*}\,\frac1p=\Bigl(\frac12+o(1)\Bigr)\log\log n ,$$

"where the $^*$ indicates that the summation is extended over all primes $p$ such that $n=kp+r$, where $p/2<r<p$ and $k$ is integral" (p. 90). In other words, the sum runs over the primes $p\le n$ whose least nonnegative residue of $n$ lies strictly between $p/2$ and $p$.

The paper proves nothing about this sum.

Source. P. Erdős, R. L. Graham, I. Z. Ruzsa and E. G. Straus, On the prime factors of $\binom{2n}{n}$, Math. Comp. 29 (1975), no. 129, 83--92; the unnumbered conjecture on p. 90. The edition is identified on the source card.

Read depth. Claims checked: the conjecture and its definition of the starred sum were read clause by clause on the page image. A conjecture has no proof to check.

Proof pointer

None; a conjecture.

Dependencies

None.

Bears on

• Problem 726: this is the problem's asymptotic as posed, the sum of $1/p$ over primes $p\le n$ with $n\bmod p\in(p/2,p)$ being asymptotic to $\frac12\log\log n$. The paper records no result on it.