What is the smallest prime?

What is the first prime? It seems that the number two should be the obvious answer, and today it is, but it was not always so. There were times when and mathematicians for whom the numbers one and three were acceptable answers. To find the first prime, we must also know what the first positive integer is. Surprisingly, with the definitions used at various times throughout history, one was often not the first positive integer (some started with two, and a few with three). In this article, we survey the history of the primality of one, from the ancient Greeks to modern times. We will discuss some of the reasons definitions changed, and provide several examples. We will also discuss the last significant mathematicians to list the number one as prime.Comment: 11 pages, 5 figure

Effect of plasma inhomogeneity on plasma wakefield acceleration driven by long bunches

Effects of plasma inhomogeneity on self-modulating proton bunches and accelerated electrons were studied numerically. The main effect is the change of the wakefield wavelength which results in phase shifts and loss of accelerated particles. This effect imposes severe constraints on density uniformity in plasma wakefield accelerators driven by long particle bunches. The transverse two stream instability that transforms the long bunch into a train of micro-bunches is less sensitive to density inhomogeneity than are the accelerated particles. The bunch freely passes through increased density regions and interacts with reduced density regions.Comment: 7 pages, 10 figure

Do all health and social care professionals interact equally: A study of interactions in multidisciplinary teams in the United Kingdom.

Problems around deficits in interprofessional collaboration have been identified since the National Health Service (NHS) was introduced. It is within the context of the current policy focus on improving collaborative working that this study was undertaken. A direct observational study using the Bales’ Interaction Process Analysis tool was carried out in two older persons teams to explore patterns of interaction in the multidisciplinary team meetings. Analysis revealed some key differences in the way in which different professions interacted. Occupational therapists, physiotherapists, social workers (SW) and nurses rarely asked for opinions and for orientation. The consultant (the individual in charge of the medical team) tended to have high rates for asking for orientation, giving opinions and giving orientation. Although some nurses did have high individual rates for the giving of orientation. The data from the research has highlighted that therapists, SWs and nurses are reluctance to voice their opinions in multidisciplinary teams and thus conformity may dominate its culture. It is suggested that therapists, SWs and nurses need to cite their opinions in teams more effectively if they are to be competent and committed patient-centred practitioners