Summary: We collect here 100 open conjectures on congruences made by the author, some of which have never been published. This is a new edition of the author’s preprint [arXiv:0911.5665] with those confirmed conjectures removed and some new conjectures added. Many congruences here are related to representations of primes by binary quadratic forms or series for powers of \(\pi\); for example, we mention two new conjectural identities
\[\sum_{n=0}^\infty {\frac{12n+1}{100^n}} \binom{2n}{n} \sum_{k=0}^n \binom{2k}{k}^2 \binom{2(n-k)}{n-k}\left (\frac{9}{4}\right)^{n-k} = \frac{75}{4\pi}\]
and
\[\sum_{k=1}^\infty \frac{3H_{k-1}^2 + 4H_{k-1}/k}{k^2\binom{2k}{k}} = \frac{\pi^4}{360} { with }H_{K-1}: = \sum_{0 < j \le k-1} \frac{1}{j}\]
and include related congruences. We hope that this paper will interest number theorists and stimulate further research.