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Prime Computer - Wikipedia, the free encyclopedia Prime Computer was a Natick, Massachusetts-based producer of minicomputers from 1972 until 1992. The Prime 400 was a successful minicomputer of its day (late 1970's) and the Prime 750 (1979) was a competitor to the DEC Vax 11/780 and was one of the first 32bit superminicomputers. By the end, not a single Prime computer was subject to COCOM export controls, as they were insufficiently powerful for the US Government to fear their falling into the hands of hostile powers. en.wikipedia.org /wiki/Prime_computer   (651 words)

Wieferich prime - Wikipedia, the free encyclopedia Wieferich primes were first described by Arthur Wieferich in 1909 in works pertaining to Fermat's last theorem. The only known Wieferich primes are 1093 and 3511 (sequence A001220 in OEIS), found by W. Prime numbers of this kind have been called Mirimanoff primes on occasion, but the name has not entered general mathematical use. en.wikipedia.org /wiki/Wieferich_prime   (502 words)

Least primitive root of prime numbers A primitive root [1] of p is a number r such that any integer a between 1 and p-1 can be expressed by a=r^k mod p, with k a nonnegative integer smaller that p-1. In fact, it is possible to relax the above conditions in order to prove that p is prime [2]; it is sufficient to find numbers r_k such that (r_k)^((p-1)/q_k) mod p>1 and (r_k)^(p-1) mod p=1 for all prime divisors q_k of p-1 (these conditions guarantee the existence of a primitive root of p). Let q_g(n) be the smallest prime number q for which g(q)=n, with n not a perfect power, and let q_G(p) and q_B(p) be defined in a similar way, with p a prime number. www.ieeta.pt /~tos/p-roots.html   (1612 words)

Irreducible and Prime Elements   (Site not responding. Last check: 2007-10-12) An element p is prime if it is a nonzero nonunit, and p divides a*b implies p divides a or p divides b. However, prime elements are usually restricted to commutative rings, unlike prime ideals, which are an important part of noncommutative ring theory, and will be addressed later. A prime integer was defined as a number that had no proper divisors, in other words, a number that could not be reduced. www.mathreference.com /ring,irr.html   (274 words)

[No title] Prime Cable amended its justification three times: on May 17, 1994; on June 27, 1994, in response to a Cable Services Bureau Order citing common deficiencies observed in benchmark filings generally; and on February 7, 1995, in response to a Cable Services Bureau Public Notice offering operators the opportunity to make optional supplemental filings. Prime Cable argues that the complaint should be dismissed because "the complainant did not describe the cable programming service nor provide a current rate for cable programming service." Prime Cable's assertion does not persuade us that the complaint is invalid or should be dismissed. Prime Cable asserts that its monthly CPS tier price of $12.03 per subscriber is justified by its benchmark filing because its price is less than the maximum permitted charge of $12.08 as calculated in its most recent amended filing, dated February 7, 1995. www.fcc.gov /ftp/Bureaus/Cable/Orders/1995/da950168.txt   (1179 words)

Number Theory Glossary A prime number is a number which has no factors other than 1 (called non-trivial factors). A number which is not prime is called composite. Thus any prime number is a pseudoprime for any base. www.math.umbc.edu /~campbell/NumbThy/Glossary.html   (946 words)

Problem 2.- Carl Pomerance Observation Pomerance observed that 210 - p is prime for p =107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197 and 199, being p all the primes such that n/2 I verified that 2310-p is prime for p=2153,2161,2179, 2203, 2207,2213, 2221, 2237, 2239, 2243, 2251, 2267, 2269, 2273, 2281,2287,2293 and 2297, being p all the prime such that 13n/14 As N and p are relatively prime (Because N=n-p www.primepuzzles.net /problems/prob_002.htm   (374 words)

CATHOLIC ENCYCLOPEDIA: Prime The name Prime (prima hora) belongs with those of Terce, Sext, None, to the short offices recited at the different hours of the day, called by these names among the Romans, that is, prima towards 6 a.m.; tertia, towards 9 a.m.; sexta, towards noon; nona towards 3 p.m. We need only remark that one of the most characteristic features of Prime is the recitation of the famous symbol "Quicumque vult salvus esse", called the Athanasian Creed, which has recently been the subject of much controversy in the Anglican Church. In view of its origin and constitution, Prime is to be considered as the prayer of the beginning of the day, whereas Lauds is devoted to recalling with the dawn the memory of Christ's Resurrection, Prime is the morning hour which consecrates all the work of the day. www.newadvent.org /cathen/12424a.htm   (928 words)

BBC NEWS | Science/Nature | Largest Prime Number discovered Mersenne primes are most relevant to number theory, but most participants join Gimps for the fun of having a role in real research - and the chance of finding a new Mersenne prime. The number 10 is not prime because it is divisible by 2 and 5. A Mersenne prime is a prime of the form 2^P-1. news.bbc.co.uk /2/hi/science/nature/3783149.stm   (621 words)

[No title] Note that it implies that only Mersenne numbers of the form 2^p for p prime can themselves be prime. For example if n is relatively prime to p-1 for some prime p, then every integer y has an nth root mod p given by the formula y^r % p where r is a multiplicative inverse of n mod p-1. Since m and n are relatively prime, there exist s and t such that sm + tn = 1. www.cs.rochester.edu /u/www/u/nelson/courses/cryptology/notes/lecture_10.txt   (970 words)

New Scientist Breaking News - Largest prime number ever is found Prime numbers are positive integers that can only be divided by themselves and one. Mersenne primes were first discussed by Euclid in 350 BC and have been central to the branch of mathematics known as number theory ever since. Primes are the building blocks of all positive numbers. www.newscientist.com /article.ns?id=dn4438   (543 words)

Profile of Coach Meyers   (Site not responding. Last check: 2007-10-12) Prime crippled Coach Meyers, breaking his arm, nose, and a leg. His urge to touch little girls was also taken away during his deposition, as Doctor Gross removed some of his hormones with a laser, undetectable by the human eye. He lost his case against California, but is trying to catch up with Prime for a day in court. marvelite.prohosting.com /ultraverse/prime/profiles/meyers.html   (224 words)

seventeen The number most often picked in response to the request "Pick a random number from 1 to 20." Seventeen is a Fermat prime (a prime number of the form 2 - 1 is prime), and the only prime that is the sum of four consecutive primes (2 + 3 + 5 + 7). Seventeen is also the smallest number for which the sum of the digits of its cube is equal to the number: 173 = 4913, 4 + 9 + 1 + 3 = 17, and the smallest number that can be written as A www.daviddarling.info /encyclopedia/S/seventeen.html   (243 words)

Comp.Sys.Prime FAQ Prime hackers keen to preserve memorabilia in their garages and spare rooms should be aware that Primos itself is actually licensed to a company or other body, not a CPU. Prime produced a machine called the Prime 200 which was compatible with the Honeywell 316 and 516 range which had just been dropped but for which there was still a demand. Prime were trying to sell big mainframes which cost a fortune to run and charging ridiculous amounts for software such as compilers, etc. What was happening was that hardware - which had been the focus of computing up to the mid 1980s - was becoming a cheap commodity. www.malch.com /prime/primefaq.htm   (19504 words)

Prime P Surnames Genealogy Society Investigating officer P Viswambharan told this website?s newspaper that the girls will be interrogated again, as there are contradictions in their statements... Prime Minister Manmohan Singh was on a tour of Vidarbha region of... The NY-P is shifting from small towns into bigger or booming markets; franchises in Brooklyn and Staten Island have thrived and a new park was built for a team... www.iaswww.com /ODP/Society/Genealogy/Surnames/P/Prime   (364 words)

Prime numbers Prime numbers and their properties were first studied extensively by the ancient Greek mathematicians. At first sight the primes seem to be distributed among the integers in rather a haphazard way. The statement that the density of primes is 1/log(n) is known as the Prime Number Theorem. www-groups.dcs.st-and.ac.uk /~history/HistTopics/Prime_numbers.html   (1600 words)

Page 9   (Site not responding. Last check: 2007-10-12) Mersenne prime numbers are in the form 2^p - 1 where p is prime. It can be proven that any number in the form of 2^p -1 where p not prime, must be composite. If p prime then the number may or may not be prime. www.geocities.com /dirkie6/page9.html   (233 words)

The Prime Puzzles and Problems Connection K consecutive primes p such that the decimal expansion of the reciprocal 1/p, for each p, has exactly a period of length (p-1) Primes p such that R(p) is prime and p^2 = R(R(p)^2) Primes such that their squares are free of the digit D. Consecutive integers with the same quantity of prime factors primepuzzles.net /puzzles   (566 words)

Prime k-tuplets   (Site not responding. Last check: 2007-10-12) All primes greater than 5 end in one of 1, 3, 7 or 9, and the four primes in a (large) quadruplet always occur in the same ten-block. A prime k-tuplet is a sequence of k consecutive prime numbers such that in some sense the difference between the first and the last is as small as possible. A prime k-tuplet is then defined as a sequence of consecutive primes {p1, p2,..., pk}such that for every prime q, not all the residues modulo q are represented by p1, p2,..., pk, and pk - p1 = s(k). www.ltkz.demon.co.uk /ktuplets.htm   (5925 words)

The Prime Glossary: Mersenne prime Primes of this form were first studied by Euclid who explored their relationship with the even perfect numbers. was prime for 2, 3, 5, 7, 13, 17, 19, 31, 67, 127, 257 and for no other primes p less than 257. Mersenne primes (sometimes just called Mersennes) are also generalized repunit primes and trivial circular primes (radix two). primes.utm.edu /glossary/page.php?sort=Mersennes   (177 words)

Prime Outlets Mall Visitors Guide - Visit Prime Outlets Mall San Marcos   (Site not responding. Last check: 2007-10-12) Prime Outlets Mall San Marcos - the largest factory outlet center in South Texas - is among the most popular travel destinations in Texas. Prime Outlets Mall San Marcos is home to a mouth-watering variety of stores, such as Dooney and Bourke, Zales, Gap Outlet, OshKosh B'Gosh, Jockey, London Fog, Polo Ralph Lauren Factory Store and Salvatore Ferragamo. Prime Outlets Mall San Marcos is also home to a food court, children's playground and ATMs. www.sanantoniocvb.com /prime_outlet_mall.asp   (319 words)

Number Theory - Project Suggestions Generate sets of  cubic residues mod p for p a prime and discuss any patterns you find. Mersenne primes are primes of the form 2 A repunit is a number whose expression consists only of 1’s, for example 11 or 111. www.geneseo.edu /~towsleyg/math319-.htm   (522 words)

[No title] prime p /\ 0 ((gcd n (p EXP a) = 1) = ~divides p n)``, S_TAC ++ MP_TAC (Q.SPECL [`p`, `n`, `a`] GCD_1_PRIME_POWERL) ++ PROVE_TAC [GCD_SYM]); val FACTOR_INDUCT = store_thm ("FACTOR_INDUCT", ``!prop. prime p /\ divides a n /\ divides p n /\ ~divides p a ==> divides a (n DIV p)``, S_TAC ++ Suff `divides (a * p DIV p) (n DIV p)` >> (Suff `0 prime p /\ 0 ((exponent p a = exponent p b) = !n. www.cs.utah.edu /~swalton/hol98/examples/miller/groups/extra_arithScript.sml   (3551 words)

Prime Patterns For example, the top number of the middle column: following are all prime; 311537, 335117, 735113, 711533, 1153, 3511..In this particular case, 31153, 71153 and 35117 are five digit primes, 11 and 53 are two digit primes, and two 3’s, the 5 and the 7 are all one digit primes. A Diigit Complementary Prime Pair is defined as a pair of prime numbers in which digits in corresponding positions sum to 10 (or 0). The prime factors of 114985 are 1, 5, 13, 29, 61. www.geocities.com /CapeCanaveral/Launchpad/4057/primes.htm   (1850 words)

Mersenne Prime Search The new prime was independently verified in 5 days by Tony Reix of Bull S.A. in Grenoble, France using 16 Itanium2 1.5 GHz CPUs of a Bull NovaScale 6160 HPC at Bull Grenoble Research Center, running the Glucas program by Guillermo Ballester Valor of Granada, Spain. The discovery is the ninth record prime for the GIMPS project. The first prime numbers are 2, 3, 5, 7, 11, etc. For example, the number 10 is not prime because it is divisible by 2 and 5. www.mersenne.org   (1054 words)

[No title] Since $N$ and $% M$ are distinct prime numbers and $-N\leq n\leq N$, $-M\leq m\leq M$, it follows that either $n=\pm N$, $m=\pm M$ or $n=m=0$. Moreover $z(-(n^{\prime },m^{\prime },s-S)),\ z(-(n^{\prime \prime },m^{\prime \prime },s-S))$ are known from step 2 of this section (see parts $(a)$, $(c)$ of Lemma 8) and $z(n^{\prime \prime }-qn,m^{\prime \prime }-qm,-S),\ z(n^{\prime }-qn,m^{\prime }-qm,-S)$ are known from Section 3. The Fourier coefficients $z(n^{\prime }-n,m^{\prime }-m,-S),\ z(n^{\prime \prime }-n,m^{\prime \prime }-m,-S)$ are known from Section 3. www.ma.utexas.edu /mp_arc/html/papers/02-286   (4728 words)

Prime Steakhouse - Las Vegas Fine Dining - Bellagio Superstar Chef Jean-Georges Vongerichten raises steakhouse dining to new heights at PRIME, located at lakeside with views of the fountains and lights of Las Vegas. Brimming with Baccarat chandeliers, plush furnishings and gilt galore, PRIME evokes the charms of a luxurious 1930s-style speakeasy. Indeed Travel and Leisure Magazine suggested, "they should issue engagement rings at the coatcheck!" Dining is permitted at Prime’s Bar. www.bellagio.com /pages/din_prime.asp   (129 words)

Theoretical Performance , which is normal multiplication modulo p, p prime, forms a cyclic group. In fact, if the prime t is chosen carefully so that p=2t+1 is also prime, all elements in the group Therefore, the following conclusions can be derived for the exponential probe function in equation (17) by applying theorem 2. www.jea.acm.org /ARTICLES/Vol2Nbr3/node11.html   (507 words)

Euclid's theorem prime p /\ p divides n ------------------------------------ 0. prime p /\ p divides 0 ------------------------------------ 0. Thus we have the hypothesis that all p beyond a certain unspecified n are not prime, and our task is to show that this cannot be. www.cl.cam.ac.uk /users/mn200/hol-tutorial/tutorial006.html   (6638 words)

PRIME homepage - Peace Research Institute in the Middle East PRIME homepage - Peace Research Institute in the Middle East PRIME is a non-governmental, nonprofit organization established by Palestinian and Israeli researchers with the help of the Peace Research Institute in Frankfurt, Germany. PRIME's purpose is to pursue mutual coexistence and peace- building through joint research and outreach activities. www.vispo.com /PRIME   (252 words)

Videos on demand Prime Minister P.J. Patterson of Jamaica, speaking at the Organization of American States (OAS) in Washington today, stressed that the Caribbean Community (CARICOM) will do “everything in its power” to ensure that Haiti is no longer isolated Diplomats greet the Prime Minister of Jamaica, during a gathering at the residence of the OAS Secretary General. The Prime Minister of Jamaica, P. Patterson, addresses a protocolary session of the OAS Permanent Council www.oas.org /OASpage/videosondemand/home_eng/videos_query.asp?sCodigo=06-0034   (317 words)

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