Primality-testing Mersenne Numbers (II)

Reports the factor-filtering and primality-testing of Mersenne Numbers Mp for p < 100000, the latter using the ICL 'DAP' Distributed Array Processor.

Mersenne Numbers: consolidated results

This document provides and comments on the results of the Lucas-Lehmer testing and/or partial factorisation of all Mersenne Numbers Mp = 2^p-1 where p is prime and less than 100,000. Previous computations have either been confirmed or corrected. The LLT computations on the ICL DAP is the first implementation of Fast-Fermat-Number-Transform multiplication in connection with Mersenne Number testing. This paper championed the disciplines of systematically testing the Mp, and of double-sourcing results which were not manifestly correct. Both disciplines were adopted by the later GIMPS initiative, the 'Great Internet Mersenne Prime Search, which was itself one of the first web-based distributed-community projects.

Developmental changes in the germinability, desiccation tolerance, hardseededness, and longevity of individual seeds of Trifolium ambiguum

Background and Aims: Using two parental clones of outcrossing Trifolium ambiguum as a potential model system, we examined how during seed development the maternal parent, number of seeds per pod, seed position within the pod, and pod position within the inflorescence influenced individual seed fresh weight, dry weight, water content, germinability, desiccation tolerance, hardseededness, and subsequent longevity of individual seeds. Methods: Near simultaneous, manual reciprocal crosses were carried out between clonal lines for two experiments. Infructescences were harvested at intervals during seed development. Each individual seed was weighed and then used to determine dry weight or one of the physiological behaviour traits. Key Results: Whilst population mass maturity was reached at 33–36 days after pollination (DAP), seed-to-seed variation in maximum seed dry weight, when it was achieved, and when maturation drying commenced, was considerable. Individual seeds acquired germinability between 14 and 44 DAP, desiccation tolerance between 30 and 40 DAP, and the capability to become hardseeded between 30 and 47 DAP. The time for viability to fall to 50 % (p50) at 60 % relative humidity and 45 °C increased between 36 and 56 DAP, when the seed coats of most individuals had become dark orange, but declined thereafter. Individual seed f. wt at harvest did not correlate with air-dry storage survival period. Analysing survival data for cohorts of seeds reduced the standard deviation of the normal distribution of seed deaths in time, but no sub-population showed complete uniformity of survival period. Conclusions: Variation in individual seed behaviours within a developing population is inherent and inevitable. In this outbreeder, there is significant variation in seed longevity which appears dependent on embryo genotype with little effect of maternal genotype or architectural factors.

Phases of dormancy in yam tubers (Dioscorea rotundata)

center dot Background and Aims The control of dormancy in yam (Disocorea spp.) tubers is poorly understood and attempts to shorten the long dormant period (i.e. cause tubers to sprout or germinate much earlier) have been unsuccessful. The aim of this study was to identify and define the phases of dormancy in Dioscorea rotundata tubers, and to produce a framework within which dormancy can be more effectively studied. center dot Methods Plants of 'TDr 131' derived from tissue culture were grown in a glasshouse simulating temperature and photoperiod at Ibadan (7 degrees N), Nigeria to produce tubers. Tubers were sampled on four occasions: 30 d before shoot senescence (149 days after planting, DAP), at shoot senescence (179 DAP), and twice during storage at a constant 25 degrees C (269 and 326 DAP). The development of the apical shoot bud was described from tissue sections. In addition, the responsiveness of shoot apical bud development to plant growth regulators (gibberellic acid, 2-chloroethanol and thiourea) applied to excised tuber sections was also examined 6 and 12 d after treatment. center dot Key Results and Conclusions Three phases of tuber dormancy are proposed: Phase I, from tuber initiation to the appearance of the tuber germinating meristem; Phase II, from the tuber germinating meristem to initiation of foliar primordium; and Phase III, from foliar primordium to appearance of the shoot bud on the surface of the tuber. Phase I is the longest phase (approx. 220 d in 'TDr 131'), is not affected by PGRs and is proposed to be an endo-dormant phase. Phases II and III are shorter (< 70 d in total), are influenced by PGRs and environmental conditions, and are therefore endo-/eco-dormant phases. To manipulate dormancy to allow off-season planting and more than one generation per year requires that the duration of Phase I is shortened.

Phases of dormancy in yam tubers (Dioscorea rotundata)

Background and Aims The control of dormancy in yam (Disocorea spp.) tubers is poorly understood and attempts to shorten the long dormant period (i.e. cause tubers to sprout or germinate much earlier) have been unsuccessful. The aim of this study was to identify and define the phases of dormancy in Dioscorea rotundata tubers, and to produce a framework within which dormancy can be more effectively studied. center dot Methods Plants of 'TDr 131' derived from tissue culture were grown in a glasshouse simulating temperature and photoperiod at Ibadan (7 degrees N), Nigeria to produce tubers. Tubers were sampled on four occasions: 30 d before shoot senescence (149 days after planting, DAP), at shoot senescence (179 DAP), and twice during storage at a constant 25 degrees C (269 and 326 DAP). The development of the apical shoot bud was described from tissue sections. In addition, the responsiveness of shoot apical bud development to plant growth regulators (gibberellic acid, 2-chloroethanol and thiourea) applied to excised tuber sections was also examined 6 and 12 d after treatment. center dot Key Results and Conclusions Three phases of tuber dormancy are proposed: Phase I, from tuber initiation to the appearance of the tuber germinating meristem; Phase II, from the tuber germinating meristem to initiation of foliar primordium; and Phase III, from foliar primordium to appearance of the shoot bud on the surface of the tuber. Phase I is the longest phase (approx. 220 d in 'TDr 131'), is not affected by PGRs and is proposed to be an endo-dormant phase. Phases II and III are shorter (< 70 d in total), are influenced by PGRs and environmental conditions, and are therefore endo-/eco-dormant phases. To manipulate dormancy to allow off-season planting and more than one generation per year requires that the duration of Phase I is shortened.