In 1967 the first set of 6 consecutive primes in arithmetic progression was found. In 1995 the first set of 7 consecutive primes in arithmetic progression was found. Between November, 1997 and March, 1998, we succeeded in finding sets of 8, 9 and 10 consecutive primes in arithmetic progression. This was made possible because of the increase in computer capability and availability, and the abili...

We investigated the role of the visual similarity of masked primes to targets in a lexical decision experiment. In the primes, some letters in the target (e.g., A in ABANDON) had either visually similar letters (e.g., H), dissimilar letters (D), visually similar digits (4), or dissimilar digits (6) substituted for them. The similarities of the digits and letters to the base letter were equated ...

The union of the straight and—of over a point reflection—reflected series arithmetic progression primes results double density occupation integer positions by multiples primes. remaining free represent diads equidistant to reflection: in case reflection is an even number, they satisfy Goldbach’s conjecture. Further, it allows prove, that number twin unlimited. all greater gaps as two between ha...

In this expository article, we describe the recent approach, motivated by ergodic theory, towards detecting arithmetic patterns in the primes, and in particular establishing in [26] that the primes contain arbitrarily long arithmetic progressions. One of the driving philosophies is to identify precisely what the obstructions could be that prevent the primes (or any other set) from behaving “ran...

It is conjectured that there exist arbitrarily long sequences of consecutive primes in arithmetic progression. In 1967, the first such sequence of 6 consecutive primes in arithmetic progression was found. Searching for 7 consecutive primes in arithmetic progression is difficult because it is necessary that a prescribed set of at least 1254 numbers between the first and last prime all be composi...

Let $q$ be a large positive integer and let $(a,q)=1$. We prove that there exist primes $p_1,p_2\le q$ number $n\le with at most two prime factors such $p_1p_2n\equiv a\pmod {q}$. This improves upon result of Shparlinski (2018).

Greek-French bilinguals were tested in three masked priming experiments with Greek primes and French targets. Related primes were the translation equivalents of target words, morphologically related to targets, or phonologically related to targets. In Experiment 1, cognate translation equivalents (phonologically similar translations) showed facilitatory priming, relative to matched phonological...