The confused Smarandache constants

The Smarandache constant x is the positive solution of 127x − 113x = 1. Its value is $x\approx 0.56714813020 \ldots$ (sequence A038458 in OEIS). Smarandache conjectured that x is in fact the smallest solution xn of $p_{n+1}^{x_n} - p_n^{x_n} =1$ as n varies, where pn is the nth prime, and interpreted this as a generalization of Andrica’s conjecture.

It should not be confused with a list of sixteen Smarandache constants denoted s1 to s16, which involve the Smarandache function S(n), defined to be the smallest integer such that S(n)! is divisible by n.

So says the Wikipedia entry on colorful, sometimes reviled mathematician and poet-mathematician-writer-philosopher Florentin Smarandache.