It was proven by Emma Lehmer that for almost all odd primes p, F2p is a Fibonacci pseudoprime. In this paper, we generalize this result to Lucas sequences {Uk}. In particular, we find Lucas sequences {Uk} for which either U2p is a Lucas pseudoprime for almost all odd primes p or Up is a Lucas pseudoprime for almost all odd primes p.

Models of written word recognition in languages using the Roman alphabet assume that a word's visual form is quickly mapped onto abstract units. This proposal is consistent with the finding that masked priming effects are of similar magnitude from lowercase, uppercase, and alternating-case primes (e.g., beard-BEARD, BEARD-BEARD, and BeArD-BEARD). We examined whether this claim can be readily ge...

We examined the effect of linguistic comprehension on early perceptual encoding in a series of electrophysiological and behavioral studies on humans. Using the fact that pictures of faces elicit a robust and reliable evoked response that peaks at ∼170 ms after stimulus onset (N170), we measured the N170 to faces that were preceded by primes that referred to either faces or scenes. When the prim...

Listeners often categorize phonotactically illegal sequences (e.g., /dla/ in English) as phonemically similar legal ones (e.g., /gla/). In an earlier investigation of such an effect in Japanese, Dehaene-Lambertz, Dupoux, and Gout (2000) did not observe a mismatch negativity in response to deviant, illegal sequences, and therefore argued that phonotactics constrain early perceptual processing. I...

This is a survey article on primality testing and general methods for recognizing primes. We also look at methods for generating random primes since this is valuable in cryptographic methods such as the RSA cipher. Mathematics Subject Classification: Primary: 11A41; Secondary: 11A51

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...