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.

In-street wind direction variability in the vicinity of a busy intersection in central London

We present results from fast-response wind measurements within and above a busy intersection between two street canyons (Marylebone Road and Gloucester Place) in Westminster, London taken as part of the DAPPLE (Dispersion of Air Pollution and Penetration into the Local Environment; www.dapple.org.uk) 2007 field campaign. The data reported here were collected using ultrasonic anemometers on the roof-top of a building adjacent to the intersection and at two heights on a pair of lamp-posts on opposite sides of the intersection. Site characteristics, data analysis and the variation of intersection flow with the above-roof wind direction (θref) are discussed. Evidence of both flow channelling and recirculation was identified within the canyon, only a few metres from the intersection for along-street and across-street roof-top winds respectively. Results also indicate that for oblique rooftop flows, the intersection flow is a complex combination of bifurcated channelled flows, recirculation and corner vortices. Asymmetries in local building geometry around the intersection and small changes in the background wind direction (changes in 15-min mean θref of 5–10 degrees) were also observed to have profound influences on the behaviour of intersection flow patterns. Consequently, short time-scale variability in the background flow direction can lead to highly scattered in-street mean flow angles masking the true multi-modal features of the flow and thus further complicating modelling challenges.

Data assimilation for marine monitoring and prediction: The MERCATOR operational assimilation systems and the MERSEA developments

During the past 15 years, a number of initiatives have been undertaken at national level to develop ocean forecasting systems operating at regional and/or global scales. The co-ordination between these efforts has been organized internationally through the Global Ocean Data Assimilation Experiment (GODAE). The French MERCATOR project is one of the leading participants in GODAE. The MERCATOR systems routinely assimilate a variety of observations such as multi-satellite altimeter data, sea-surface temperature and in situ temperature and salinity profiles, focusing on high-resolution scales of the ocean dynamics. The assimilation strategy in MERCATOR is based on a hierarchy of methods of increasing sophistication including optimal interpolation, Kalman filtering and variational methods, which are progressively deployed through the Syst`eme d’Assimilation MERCATOR (SAM) series. SAM-1 is based on a reduced-order optimal interpolation which can be operated using ‘altimetry-only’ or ‘multi-data’ set-ups; it relies on the concept of separability, assuming that the correlations can be separated into a product of horizontal and vertical contributions. The second release, SAM-2, is being developed to include new features from the singular evolutive extended Kalman (SEEK) filter, such as three-dimensional, multivariate error modes and adaptivity schemes. The third one, SAM-3, considers variational methods such as the incremental four-dimensional variational algorithm. Most operational forecasting systems evaluated during GODAE are based on least-squares statistical estimation assuming Gaussian errors. In the framework of the EU MERSEA (Marine EnviRonment and Security for the European Area) project, research is being conducted to prepare the next-generation operational ocean monitoring and forecasting systems. The research effort will explore nonlinear assimilation formulations to overcome limitations of the current systems. This paper provides an overview of the developments conducted in MERSEA with the SEEK filter, the Ensemble Kalman filter and the sequential importance re-sampling filter.

Formation of dityrosine cross-links during breadmaking

To establish its significance during commercial breadmaking, dityrosine formation was quantified in flours and doughs of six commercial wheat types at various stages of the Chorleywood Bread Process. Dityrosine was formed mainly during mixing and baking, at the levels of nmol/g dry weight. Good breadmaking flours tended to exhibit higher dityrosine content in the final bread than low quality ones, but no relationship was found for dityrosine as a proportion of flour protein content, indicating that the latter was still a dominant factor in the analysis. There was no correlation between gluten yield of the six wheat types and their typical dityrosine concentrations, suggesting that dityrosine crosslinks were not a determinant factor for gluten formation. Ascorbic acid was found to inhibit dityrosine formation during mixing and proving, and have no significant effect on dityrosine in the final bread. Hydrogen peroxide promoted dityrosine formation, which suggests a radical mechanism involving endogenous peroxidases might be the responsible for dityrosine formation during breadmaking.