Megacam Photometric Calibration
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Elementary Proof That an Infinite Number of Cullen Primes Exist
Elementary Proof that an Infinite Number of Cullen Primes Exist Stephen Marshall 21 February 2017 Abstract This paper presents a complete proof of the Cullen Primes are infinite, even though only 16 of them have been found as of 21 Feb 2017. We use a proof found in Reference 1, that if p > 1 and d > 0 are integers, that p and p+ d are both primes if and only if for integer m: m = (p-1)!( + ) + + We use this proof for d = to prove the infinitude of Cullen prime numbers. The author would like to give many thanks to the authors of 1001 Problems in Classical Number Theory, Jean-Marie De Koninck and Armel Mercier, 2004, Exercise Number 161 (see Reference 1). The proof provided in Exercise 6 is the key to making this paper on the Cullen Prime Conjecture possible. Introduction James Cullen, (19 April 1867 – 7 December 1933) was born at Drogheda, County Louth, Ireland. At first he was educated privately, then he studied pure and applied mathematics at the Trinity College, Dublin for a while, he went to 1 Mungret College, Limerick, before deciding to become a Jesuit, studying in England in Mansera House, and St. Mary's, and was ordained as a priest on 31 July 1901. In 1905, he taught mathematics at Mount St. Mary's College in Derbyshire and published his finding of what is now known as Cullen numbers in number theory. In number theory of prime numbers, a Cullen number is a natural number of the form n Cn = n2 + 1 Cullen numbers were first studied by James Cullen in 1905. -
X22a CFHT Megaprime U-Band Source Catalog of the AKARI North Ecliptic Pole Field
2020 Autumn Annual Meeting, Astronomical Society of Japan X22a CFHT Megaprime u-band Source Catalog of the AKARI North Ecliptic Pole Field Ting-Chi Huang (SOKENDAI, ISAS/JAXA), Hideo Matsuhara (SOKENDAI, ISAS/JAXA), To- motsugu Goto (NTHU), Tetsuya Hashimoto (NTHU), Seong-Jin Kim (NTHU), Nagisa Oi (TUS), Hyunjin Shim (KNU), Ho Seong Hwang (KASI), Yoshiki Toba (Kyoto Univ.), Daryl Joe D. Santos (NTHU), and Toshinobu Takagi (JSF) AKARI infrared (IR) space telescope carried out a survey in the North Ecliptic Pole (NEP) field using its Infrared Camera (IRC), and detected more than 100,000 IR sources. AKARI IRC’s 9 filters continuously cover the wavelength from near- to mid-IR, making AKARI unique in comparison with other IR space telescopes like Spitzer or WISE. However, the research in the AKARI NEP field was limited due to the lack of sufficient optical and ultraviolet (UV) observations. Recently, we have performed an observation in the AKARI NEP field using Subaru HSC, and obtained deep optical images. Now we further provide the near-UV (u band) catalog from Canada-France-Hawaii Telescope (CFHT) Megaprime to assist the precious AKARI data. The observation was conducted in 7 nights under the Queued Service Observations mode in 2015 and 2016, and covered a 3.6-deg2 area. The data were processed by the Elixir pipeline, and the mosaic image was created by the AstrOmatic software. Compared with previous work, this work not only extends the area coverage to the whole AKARI NEP field, but also reaches a deeper imaging, which is a significant improvement for us to estimate photometric redshifts of galaxies or study stellar populations.. -
Largest Prime Number Pdf
Largest prime number pdf Continue The largest known downtime number (as of this October 2020) is 282,589,933 1, a number that has 24,862,048 figures when written in base 10. It was found using a computer volunteered by Patrick Laroche of the Great Internet Mersenne Prime Search (GIMPS) in 2018. The plot of 2020 with the number of numbers in the biggest known prime of the year, starting with an electronic computer. Vertical scale logarithic. A simple number is a positive integer without divisions, except for one and yourself, except for one. Euclid recorded proof that there is no singlest number, and many mathematicians and amateurs continue to look for big numbers. Many of the biggest known primes of Mersenn are primes, numbers that are one less than the power of two. By the largest in December 2018, the eight largest known primes are Mersenne primes. The last seventeen prime ministers were Mersenne primes. The binary representation of any Prime Minister of Merschenn consists of all 1, since the binary form of 2k is 1 simply k 1's. Fourier's rapid transformation in the Lucas- Lemer primaryity test for Merseynna numbers is quickly compared to other known primary tests for other types of numbers. The current record record is currently at 282,589,933 and 1 with 24,862,048 figures found by GIMPS in December 2018. Its value: 148894445742041325547806458472397979166627399279279927953241852712894252139393610644753103099711313118033717475283444014144014235875560 ... (24,861,808 figures omitted)... 062107555579479582975151595208808807192693676521782181726409111153081919192693633366558 The Great Internet Mersenne Prime Search (GIMPS) is currently offering US$3,000 research discovery award to participants who download and run their free software and whose computer discovers the new Mersenne Prime with less than 100 million digits. -
Cytiva Amersham Megaprime DNA Labeling Systems Manual
GE Healthcare Amersham Megaprime DNA Labeling Systems Product Booklet Codes: RPN1604 RPN1605 RPN1606 RPN1607 Page finder 1. Legal 3 2. Handling 4 2.1. Safety warnings and precautions 4 2.2. Storage and stability 4 2.3. Quality control 4 3. System components 6 3.1. Megaprime DNA Labeling Systems 8 4. Introduction 9 5. Megaprime DNA labeling protocols 11 5.1. Standard Megaprime protocol 11 5.2. New Megaprime protocol 15 5.3. Use of alternative reaction conditions 20 6. Appendices 27 6.1. Appendix I. Labeling of DNA fragments in low melting point agarose 27 6.2. Appendix II. Monitoring the reaction and calculating the specific activity of the labeled DNA 28 6.3. Appendix III. Removal of unincorporated nucleotides 32 6.4. Appendix IV. Additional equipment and reagents 34 7. Troubleshooting guide 35 8. References 38 9. Related products 39 2 1. Legal GE, imagination at work and GE monogram are trademarks of General Electric Company. Amersham, Megaprime, Hybond, Hyperfilm, Hypercassette, Hyperscreen, Rapid-hyb, Ready-To-Go, Rediprime, Sensitize, Sephadex and TrackerTape are trademarks of GE Healthcare companies. All third party trademarks are the property of their respective owners. © 2002–2010 General Electric Company – All rights reserved. First published 2002 All goods and services are sold subject to the terms and conditions of sale of the company within GE Healthcare which supplies them. A copy of these terms and conditions is available on request Contact your local GE Healthcare representative for the most current information. http://www.gelifesciences.com GE Healthcare UK Limited. Amersham Place, Little Chalfont, Buckinghamshire, HP7 9NA UK 3 2. -
Subject Index
Subject Index Many of these terms are defined in the glossary, others are defined in the Prime Curios! themselves. The boldfaced entries should indicate the key entries. γ 97 Arecibo Message 55 φ 79, 184, see golden ratio arithmetic progression 34, 81, π 8, 12, 90, 102, 106, 129, 136, 104, 112, 137, 158, 205, 210, 154, 164, 172, 173, 177, 181, 214, 219, 223, 226, 227, 236 187, 218, 230, 232, 235 Armstrong number 215 5TP39 209 Ars Magna 20 ASCII 66, 158, 212, 230 absolute prime 65, 146, 251 atomic number 44, 51, 64, 65 abundant number 103, 156 Australopithecus afarensis 46 aibohphobia 19 autism 85 aliquot sequence 13, 98 autobiographical prime 192 almost-all-even-digits prime 251 averaging sets 186 almost-equipandigital prime 251 alphabet code 50, 52, 61, 65, 73, Babbage 18, 146 81, 83 Babbage (portrait) 147 alphaprime code 83, 92, 110 balanced prime 12, 48, 113, 251 alternate-digit prime 251 Balog 104, 159 Amdahl Six 38 Balog cube 104 American Mathematical Society baseball 38, 97, 101, 116, 127, 70, 102, 196, 270 129 Antikythera mechanism 44 beast number 109, 129, 202, 204 apocalyptic number 72 beastly prime 142, 155, 229, 251 Apollonius 101 bemirp 113, 191, 210, 251 Archimedean solid 19 Bernoulli number 84, 94, 102 Archimedes 25, 33, 101, 167 Bernoulli triangle 214 { Page 287 { Bertrand prime Subject Index Bertrand prime 211 composite-digit prime 59, 136, Bertrand's postulate 111, 211, 252 252 computer mouse 187 Bible 23, 45, 49, 50, 59, 72, 83, congruence 252 85, 109, 158, 194, 216, 235, congruent prime 29, 196, 203, 236 213, 222, 227, -
A-Primer-On-Prime-Numbers.Pdf
A Primer on Prime Numbers Prime Numbers “Prime numbers are the very atoms of arithmetic. The primes are the jewels studded throughout the vast expanse of the infinite universe of numbers that mathematicians have studied down the centuries.” Marcus du Sautoy, The Music of the Primes 2 • Early Primes • Named Primes • Hunting for Primes • Visualizing Primes • Harnessing Primes 3 Ishango bone The Ishango bone is a bone tool, dated to the Upper Paleolithic era, about 18,000 to 20,000 BC. It is a dark brown length of bone, the fibula of a baboon, It has a series of tally marks carved in three columns running the length of the tool Note: image is 4 reversed A History and Exploration of Prime Numbers • In the book How Mathematics Happened: The First 50,000 Years, Peter Rudman argues that the development of the concept of prime numbers could have come about only after the concept of division, which he dates to after 10,000 BC, with prime numbers probably not being understood until about 500 BC. He also writes that "no attempt has been made to explain why a tally of something should exhibit multiples of two, prime numbers between 10 and 20,… Left column 5 https://en.wikipedia.org/wiki/Ishango_bone Euclid of Alexandria 325-265 B.C. • The only man to summarize all the mathematical knowledge of his times. • In Proposition 20 of Book IX of the Elements, Euclid proved that there are infinitely many prime numbers. https://en.wikipedia.org/wiki/Euclid 6 Eratosthenes of Cyrene 276-194 B.C. -
Activation of Antigen-Specific Cytotoxic T Lymphocytes by Β2-Microglobulin Or TAP1 Gene Disruption and the Introduction of Recipient-Matched MHC Class I Gene in Allogeneic
Activation of Antigen-Specific Cytotoxic T Lymphocytes by β2-Microglobulin or TAP1 Gene Disruption and the Introduction of Recipient-Matched MHC Class I Gene in This information is current as Allogeneic Embryonic Stem Cell-Derived of October 2, 2021. Dendritic Cells Yusuke Matsunaga, Daiki Fukuma, Shinya Hirata, Satoshi Fukushima, Miwa Haruta, Tokunori Ikeda, Izumi Negishi, Yasuharu Nishimura and Satoru Senju Downloaded from J Immunol 2008; 181:6635-6643; ; doi: 10.4049/jimmunol.181.9.6635 http://www.jimmunol.org/content/181/9/6635 http://www.jimmunol.org/ References This article cites 41 articles, 22 of which you can access for free at: http://www.jimmunol.org/content/181/9/6635.full#ref-list-1 Why The JI? Submit online. • Rapid Reviews! 30 days* from submission to initial decision by guest on October 2, 2021 • No Triage! Every submission reviewed by practicing scientists • Fast Publication! 4 weeks from acceptance to publication *average Subscription Information about subscribing to The Journal of Immunology is online at: http://jimmunol.org/subscription Permissions Submit copyright permission requests at: http://www.aai.org/About/Publications/JI/copyright.html Email Alerts Receive free email-alerts when new articles cite this article. Sign up at: http://jimmunol.org/alerts The Journal of Immunology is published twice each month by The American Association of Immunologists, Inc., 1451 Rockville Pike, Suite 650, Rockville, MD 20852 Copyright © 2008 by The American Association of Immunologists All rights reserved. Print ISSN: 0022-1767 -