Two studies examined the effects of implicit and explicit priming of aging stereotypes. Implicit primes had a significant effect on older adults' memory, with positive primes associated with greater recall than negative primes. With explicit primes, older adults were able to counteract the impact of negative stereotypes when the cues were relatively subtle, but blatant stereotype primes suppres...

Twin primes are primes of the form (p, p + 2). There are many proofs for the infinitude of prime numbers, but it is very difficult to prove whether there are an infinite number of pairs of twin primes. Most mathemati­ cians agree that the evidence points toward this conclusion, but numerous attempts at a proof have been falsified by subsequent review. The prob­ lem itself, one of the most famou...

This paper discusses the factorization of the RSA modulus N (i.e., N = pq, where p, q are primes of same bit size) by reconstructing the primes from randomly known bits. The reconstruction method is a modified brute-force search exploiting the known bits to prune wrong branches of the search tree, thereby reducing the total search space towards possible factorization. Here we revisit the work o...

A modiication of Katzman's example is given to produce a two-generated ideal in a two-dimensional Noetherian integral domain for which the set of associated primes of all the Frobenius powers is innnite. A further modiication yields a four-dimensional Noetherian integral domain and a ve-dimensional Noetherian local integral domain for which an explicit second local cohomology module has innnite...

Prime numbers have fascinated people since ancient times. Since the last century, their study has acquired importance also on account of the crucial role played by them in cryptography and other related areas. One of the problems about primes which has intrigued mathematicians is whether it is possible to have long strings of primes with the successive primes differing by a fixed number, namely...

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...