Mersenne numbers

These notes have been issued on a small scale in 1983 and 1987 and on request at other times. This issue follows two items of news. First, WaIter Colquitt and Luther Welsh found the 'missed' Mersenne prime M110503 and advanced the frontier of complete Mp-testing to 139,267. In so doing, they terminated Slowinski's significant string of four consecutive Mersenne primes. Secondly, a team of five established a non-Mersenne number as the largest known prime. This result terminated the 1952-89 reign of Mersenne primes. All the original Mersenne numbers with p < 258 were factorised some time ago. The Sandia Laboratories team of Davis, Holdridge & Simmons with some little assistance from a CRAY machine cracked M211 in 1983 and M251 in 1984. They contributed their results to the 'Cunningham Project', care of Sam Wagstaff. That project is now moving apace thanks to developments in technology, factorisation and primality testing. New levels of computer power and new computer architectures motivated by the open-ended promise of parallelism are now available. Once again, the suppliers may be offering free buildings with the computer. However, the Sandia '84 CRAY-l implementation of the quadratic-sieve method is now outpowered by the number-field sieve technique. This is deployed on either purpose-built hardware or large syndicates, even distributed world-wide, of collaborating standard processors. New factorisation techniques of both special and general applicability have been defined and deployed. The elliptic-curve method finds large factors with helpful properties while the number-field sieve approach is breaking down composites with over one hundred digits. The material is updated on an occasional basis to follow the latest developments in primality-testing large Mp and factorising smaller Mp; all dates derive from the published literature or referenced private communications. Minor corrections, additions and changes merely advance the issue number after the decimal point. The reader is invited to report any errors and omissions that have escaped the proof-reading, to answer the unresolved questions noted and to suggest additional material associated with this subject.

Effects of host plant drought stress on the performance of the bird cherry-oat aphid, Rhopalosiphum padi (L.): a mechanistic analysis

1. The growth (increase in height and leaf number) of four grass species was reduced by a -0.5 MPa drought stress, but the performance of an associated herbivore, Rhopalosiphum padi (L.), was not affected consistently. The intrinsic rate of increase of R. padi was reduced by drought stress on three grass species, including Dactylis glomerata (L.), but was unaffected on Arrhenatherum elatius (L.). Therefore, there is no general relationship in the effect of plant drought on an insect herbivore, even among closely related host plant species. 2. Drought stress increased the quality of plant phloem sap, as indicated by increased sieve element osmotic pressure and essential amino acid concentrations. Thus, diet quality could not account for the reduced performance of R. padi under drought stress. The concentration of essential amino acids in the phloem of well-watered A. elatius was, however, lower than that of well-watered D. glomerata, correlating with the decreased performance of aphids on well-watered A. elatius. 3. There were no differences in aphid feeding duration between watering treatments or plant species but sap ingestion rates were reduced significantly under drought stress. 4. Using the measure of dietary amino acid concentrations and the estimate of sap ingestion, the essential amino acid flux through aphids was calculated. Compared with the flux through aphids feeding on well-watered D. glomerata, there was a reduction in aphids feeding on drought-stressed D. glomerata and drought-stressed A. elatius due to lower sap ingestion rates. The flux through aphids on well-watered A. elatius was also reduced due to low phloem essential amino acid concentrations. Thus, the performance of an aphid is correlated with the availability and accessibility of essential amino acids.

A simple and rapid method for preserving RNA of aquatic invertebrates for ecotoxicogenomics

Here we describe a novel, inexpensive and simple method for preserving RNA that reduces handling stress in aquatic invertebrates following ecotoxicogenomic experimentation. The application of the method is based on transcriptomic experiments conducted on Daphnia magna, but may easily be applied on a range of other aquatic organisms of a particular size with e.g. amphipod Gammarus pulex representing an upper size limit. We explain in detail how to apply this new method, named the "Cylindrical Sieve (CS) system", and highlight its advantages and disadvantages.

An improved methodology for the recovery of Zea mays and other large crop pollen, with implications for environmental archaeology in the Neotropics

We present a simple sieving methodology to aid the recovery of large cultigen pollen grains, such as maize (Zea mays L.), manioc (Manihot esculenta Crantz), and sweet potato (Ipomoea batatas L.), among others, for the detection of food production using fossil pollen analysis of lake sediments in the tropical Americas. The new methodology was tested on three large study lakes located next to known and/or excavated pre-Columbian archaeological sites in South and Central America. Five paired samples, one treated by sieving, the other prepared using standard methodology, were compared for each of the three sites. Using the new methodology, chemically digested sediment samples were passed through a 53 µm sieve, and the residue was retained, mounted in silicone oil, and counted for large cultigen pollen grains. The filtrate was mounted and analysed for pollen according to standard palynological procedures. Zea mays (L.) was recovered from the sediments of all three study lakes using the sieving technique, where no cultigen pollen had been previously recorded using the standard methodology. Confidence intervals demonstrate there is no significant difference in pollen assemblages between the sieved versus unsieved samples. Equal numbers of exotic Lycopodium spores added to both the filtrate and residue of the sieved samples allow for direct comparison of cultigen pollen abundance with the standard terrestrial pollen count. Our technique enables the isolation and rapid scanning for maize and other cultigen pollen in lake sediments, which, in conjunction with charcoal and pollen records, is key to determining land-use patterns and the environmental impact of pre-Columbian societies.

Cacao swollen shoot virus in Nigeria: analysis of a pathogen and its vectors

Cacao swollen shoot virus (CSSV) causes the Cacao swollen shoot virus disease (CSSVD) and significantly reduces production in West African cacao. This study characterised the current status of the disease in the major cacao growing States in Nigeria and attempted a clarification on the manner of CSSV transmission. Two separate field surveys and sample collections were conducted in Nigeria in summer 2012 and spring 2013. PCR-based screening of cacao leaf samples and subsequent DNA sequencing showed that the disease continues to persist in Ondo and Oyo States and in new cacao sites in Abia, Akwa Ibom, Cross River and Edo States. Mealybug samples collected were identified using a robust approach involving environmental scanning electron microscopy, histology and DNA barcoding, which highlighted the importance of integrative taxonomy in the study. The results show that the genus Planococcus (Planococcus citri (Risso) and/or Planococcus minor (Maskell)) was the most abundant vector (73.5%) at the sites examined followed by Formicococcus njalensis (Laing) (19.0 %). In a laboratory study, the feeding behaviour of Pl. citri, Pseudococcus longispinus (Targioni-Tozzetti) and Pseudococcus viburni (Signoret) on cacao were investigated using electrical penetration graph (EPG) analysis. EPG waveforms reflecting intercellular stylet penetration (C), extracellular salivation (E1e), salivation in sieve elements (E1), phloem ingestion (E2), derailed stylet mechanics (F), xylem ingestion (G) and non-probing phase (Np) were analysed. Individual mealybugs exhibited marked variation within species and significantly differed (p ≤ .05) between species for E1e and E1. PCR-based assessments of the retention time for CSSV in viruliferous Pl. citri, Ps. longispinus and Ps. viburni fed on a non-cacao diet showed that CSSV was still detectable after 144 hours. These unusually long durations for a pathogen currently classified as a semi-persistent virus have implications for the design of non-malvaceous barrier crops currently being considered for the protection of new cacao plantings.