A. O. L. Atkin

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The aim of this paper is to describe the theory and implementation of the Elliptic Curve Primality Proving algorithm. Problema, números primos a compositis dignoscendi, hosque in factores suos primos resolvendi, ad gravissima ac utilissima totius arithmeticae pertinere, et geometrarum turn veterum turn recentiorum industriam ac sagacitatem occupavisse, tarn(More)
#(571+4) = 0 (mod 5), (1.1) p{ln+5) == 0(mod7), (1.2) p{Un+6) = 0 (mod 11). (1.3) All existing proofs of these results appeal to the theory of generating functions, and provide no method of actually separating the partitions concerned into q equal classes {q = 5, 7, or 11). Dyson (1) discovered empirically a remarkable combinatorial method of dividing the(More)
Colonization by the fungal pathogen Candida albicans varies significantly, depending upon the pH and availability of oxygen. Because of our interest in extracellular molecules as potential quorum-sensing molecules, we examined the physiological conditions which regulate the production of the aromatic alcohols, i.e., phenethyl alcohol, tyrosol, and(More)
In yeast, the accelerated rate of decay of nonsense mutant mRNAs, called nonsense-mediated mRNA decay, requires three proteins, Upf1p, Upf2p, and Upf3p. Single, double, and triple disruptions of the UPF genes had nearly identical effects on nonsense mRNA accumulation, suggesting that the encoded proteins function in a common pathway. We examined the(More)
In Saccharomyces cerevisiae the UPF1 protein is required for nonsense-mediated mRNA decay, the accelerated turnover of mRNAs containing a nonsense mutation. Several lines of evidence suggest that translation plays an important role in the mechanism of nonsense mRNA decay, including a previous report that nonsense mRNAs assemble in polyribosomes. In this(More)
The opportunistic fungal pathogen Candida albicans is a part of the normal flora but it also causes systemic candidiasis if it reaches the bloodstream. Upon being phagocytized by macrophages, an important component of innate immunity, C. albicans rapidly upregulates a set of arginine biosynthetic genes. Arginine, urea, and CO2 induced hyphae in a(More)
Vestigial mutants are associated with imaginal disc cell death which results in the deletion of adult wing and haltere structures. The vestigial locus has previously been cloned, and mutational lesions associated with a number of vg alleles were mapped within a 19 kb DNA region defined as essential for vg function. Herein we report the identification and(More)
The nonsense-mediated mRNA decay (NMD) pathway, present in most eukaryotic cells, is a specialized pathway that leads to the recognition and rapid degradation of mRNAs with premature termination codons and, importantly, some wild-type mRNAs. Earlier studies demonstrated that aberrant mRNAs with artificially extended 3'-untranslated regions (3'-UTRs) are(More)