A number p is a safe prime if both p and (p − 1)/2 are prime. This note describes a method of generating safe primes that is considerably faster than repeatedly generating random primes q until p = 2q + 1 is also prime.

Diabetes mellitus has been shown to be associated with heart failure of unknown origin, which is termed ‘diabetic w x w x cardiomyopathy’ 1 . Regan et al. 2 have shown that the small vessel lesions in diabetes mellitus have little or no relation to diabetic cardiomyopathy, suggesting that the contractile function of the diabetic cardiomyopathy was primarily defective. Although many studies have...

Immunoassay Team, Edinburgh EHI 2Q W, Scotland Lawrence M. Killingsworth, Clinical Chemistry and Immunology Laboratories, Sacred Heart Medical Center, Spokane, WA 99220 Phillipe Sizaret, Division of Environmental Carcinogenesis, International Agency for Research on Cancer, Lyon Cedex 2, France Assigned Judith A. Clayton-Hopkins, Abbott Laboratories, Editor: North Chicago, IL 60064 (formerly at ...

We construct arcs K of cardinality 2q + 1 in the projective space PG(3, q3), q = ph, p > 3 prime, from a cubic curve C. By construction, K is stabilized by a p-Sylow subgroup of the projectivities preserving C and it is contained in no twisted cubic of PG(3, q3). Mathematics Subject Classification: 51A30, 51E20, 51E21

This is a largely expository paper, providing self-contained account on the results of Schäfke and Singer (2017, 2019), in cases denoted there 2Q 2M. These papers supplied new proofs to main theorems Adamczewski Bell (2017) Bézivin Boutabaa (1992), rationality power series satisfying pair independent $q$-difference, or Mahler, equations. We emphasize language $\Gamma$ -difference modules, inste...

Let p be prime and q|p − 1. Suppose xq ≡ a(mod p) has a solution. We estimate the size of the smallest solution x0 with 0 < x0 < p. We prove that |x0| p3/2q−1 log p. By applying the Burgess character sum estimates, and estimates of certain exponential sums due to Bourgain, Glibichuk and Konyagin, we derive refinements of our result.

Safe primes are prime numbers of the form p = 2q +1 where q is prime. This note introduces a simple method for doubling the speed of safe prime generation. The method is particularly suited to settings where a large number of RSA moduli must be generated. keywords : safe primes, key-generation, prime-generation, RSA.

For a smooth surface X in P of degree d, defined over a finite field Fq with q elements, q prime, we prove that X has at most d(d+q−1)(d+2q−2)/6+d(11d−24)(q+1) points with coordinates in Fq.

We obtain the rate of decay of the smallest eigenvalue of the Hankel matrices R I t j+kW 2 (t) dt n j;k=0 for a general class of even exponential weights W 2 = exp ( 2Q) on an interval I. More precise asymptotics for more special weights have been obtained by many authors. Remark 1 Running Title: Smallest Eigenvalues of Hankel Matrices