Three experiments examined the time course of layout priming with photographic scenes varying in complexity (number of objects). Primes were presented for varying durations (800-50 ms) before a target scene with 2 spatial probes; observers indicated whether the left or right probe was closer to viewpoint. Reaction time was the main measure. Scene primes provided maximum benefits with 200 ms or ...

For small odd primes p, we prove that most of the rational points on the modular curve X0(p)/wp parametrize pairs of elliptic curves having infinitely many supersingular primes. This result extends the class of elliptic curves for which the infinitude of supersingular primes is known. We give concrete examples illustrating how these techniques can be explicitly used to construct supersingular p...

Motivated by recent work of Drmota, Mauduit and Rivat, we discuss the possibility of counting the number of primes up to x whose sum of digits is also prime. We show that, although this is not possible unless we assume a hypothesis on the distribution of primes stronger than what is implied by the Riemann hypothesis, we can establish a Mertens-type result. That is, we obtain a formula for the n...

The beauty of these relationships is that, by inspection alone, one may instantly observe whether or not a prime number is = 1, or = 3 (mod 4). These relationships are especially valuable for very large prime numbers-such as the larger Mersenne primes. Thus, it is seen from inspection of the penultimate digits of the Mersenne primes, as given in [1 ] , that all of the given primes are = 3 (mod ...

We introduce a method for showing that there exist prime numbers which are very close together. The method depends on the level of distribution of primes in arithmetic progressions. Assuming the Elliott-Halberstam conjecture, we prove that there are infinitely often primes differing by 16 or less. Even a much weaker conjecture implies that there are infinitely often primes a bounded distance ap...

Over 25 years ago, the first author conjectured in [15] that the existence of arbitrarily large primes is provable from the axioms IΔ0( ) + def( ), where (x) is the number of primes not exceeding x, IΔ0( ) denotes the theory of Δ0 induction for the language of arithmetic including the new function symbol , and def( ) is an axiom expressing the usual recursive definition of . We prove a modified...

In this lecture celebrating the 150th anniversary of the seminal paper of Riemann, we discuss various approaches to interesting questions concerning the distribution of primes, including several that do not involve the Riemann zeta-function. 1. The prime number theorem, from the beginning By studying tables of primes, Gauss understood, as a boy of 15 or 16 (in 1792 or 1793), that the primes occ...

Finding mathematical proofs for easily observed properties of the distribution of prime numbers is a difficult and often humbling task, at least for the authors of this paper. The twin prime conjecture is a famous example of this, but we are concerned here with the much more modest problem of proving that there are arbitrarily large primes that are “unusually close ” together. Statistically thi...

The present study was an attempt to replicate and extend Brown's (1979) finding of inhibition in retrieval from semantic memory produced by presentation of semantically related primes. Subjects' speed and accuracy in answering generalknowledge questions (e.g., Who was the first man to walk on the moon?) were measured when the question was preceded by one of four different prime types: neutral (...

Two masked priming experiments examined behavioural and event-related potential responses to simplex target words (e.g., flex) preceded by briefly presented, masked, derived word primes (flexible-flex), complex nonword primes formed by an illegal combination of the target word and a real suffix (flexify-flex), and simplex nonword primes formed by adding a nonsuffix word ending to the target (fl...