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Topic: Lucky primes

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	math lessons - Lucky number
		A lucky number is a natural number in a set which is generated by a "sieve" similar to the Sieve of Eratosthenes that generates the primes.
		Lucky numbers share some properties with primes, such as asymptotic behaviour according to the prime number theorem; also Goldbach's conjecture has been extended to them.
		Sloane, Neil J. A sequence of lucky primes - A031157: http://www.research.att.com/cgi-bin/access.cgi/as/njas/sequences/eisA.cgi?Anum=031157
	www.mathdaily.com /lessons/Lucky_number (336 words)

	Lucky prime - Wikipedia, the free encyclopedia
		A lucky prime is a number that is a prime number and a lucky number.
		Twin lucky primes occur less often than twin primes in general, but in a similar proportion.
		Twin primes are primes which are separated by two (example 5 and 7); these are only rare due to the methods by which lucky numbers are determined.
	en.wikipedia.org /wiki/Lucky_prime (147 words)

	lucky number
		Also, the gaps between successive primes and the gaps between successive luckies widen at roughly the same rate as the numbers increase, and the number of twin primes – primes that differ by 2 – is close to the number of twin luckies.
		The luckies even have their own equivalent of the famous (still unsolved) Goldbach Conjecture, which states that every even number greater than 2 is the sum of two primes.
		In the case of luckies, it is conjectured that every even number is the sum of two luckies; no exception has yet been found.
	www.daviddarling.info /encyclopedia/L/lucky_number.html (367 words)

	Lucky number - Wikipedia, the free encyclopedia
		A lucky number is a natural number in a set which is generated by a "sieve" similar to the Sieve of Eratosthenes that generates the primes.
		Lucky numbers share some properties with primes, such as asymptotic behaviour according to the prime number theorem; also Goldbach's conjecture has been extended to them.
		Because of these apparent connections with the prime numbers, some mathematicians have suggested that these properties may be found in a larger class of sets of numbers generated by sieves of a certain unknown form, although there is little theoretical basis for this conjecture.
	en.wikipedia.org /wiki/Lucky_number (385 words)

	kleppinger (Site not responding. Last check: 2007-10-20)
		The lucky number sieve is a modification of the prime number sieve.
		The fundamental difference between prime and lucky numbers is that while the prime number sieve is based on divisibility properties, the lucky number sieve is based purely on a number’s position in a given sequence.
		The densities of luckies and primes in large, closed intervals are very close, as are the numbers of twin primes and twin luckies (numbers differing only by 2).
	www.brynmawr.edu /scienceresearch/kleppinger.html (262 words)

	Prime Number -- from Wolfram MathWorld
		Prime numbers can be generated by sieving processes (such as the sieve of Eratosthenes), and lucky numbers, which are also generated by sieving, appear to share some interesting asymptotic properties with the primes.
		prime factors of a given integer, a process known as factorization or prime factorization.
		Primes consisting of digits that are themselves primes include 23, 37, 53, 73, 223, 227, 233, 257, 277, 337, 353, 373, 523, 557,...
	mathworld.wolfram.com /PrimeNumber.html (2014 words)

	PalPrimePage 5
		A030463 Previous palindromic prime concatenated with this palindromic prime is prime.
		A053600 a(n+1) is the smallest palindromic prime with a(n) as a central substring.
		A054217 Prime p concatenated with its emirp p' (prime reversal) makes a palindromic prime of the form 'primemirp' (rightmost digit of p and leftmost digit of p' are blended together - p and p' palindromic allowed).
	www.worldofnumbers.com /palprim5.htm (2267 words)

	Prime Numbers and Twin Primes - National Curve Bank
		Thus, the distribution of primes is closely related to one of the most renowned unsolved questions in mathematics, the Riemann hypothesis, which concerns an infinite sum of numbers called the Zeta function.
		The NCB was lucky to have had his timely Deposit # 19 a few weeks before the announcement of Goldston and Yildrim's new work.
		This prime was found by Josh Findley of the National Oceanic and Atmospheric Administration.
	curvebank.calstatela.edu /prime/prime.htm (596 words)

	NOVA \| scienceNOW \| Seven Prime Questions \| PBS
		A prime number is a number greater than one, a whole number whose only divisors—the only numbers that divide evenly into it—are itself and one.
		So three is a prime but six is not because two and three both divide into six.
		And whenever you have a pair of primes that differ by two, that's called a twin prime.
	www.pbs.org /wgbh/nova/sciencenow/3302/02-numb-nf.html (727 words)

	Mersenne Prime Search
		The new prime at 9,808,358 digits is 650,000 digits larger than their previous record prime found last December.
		The new prime was independently verified in 6 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 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 (977 words)

	Arithmetic, Numeration, Number Theory - Numericana
		Prime factorizations: Resolving composite integers into their prime factors.
		A prime number of that shape (i.e., one unit less than a power of 2) is known as a Mersenne prime.
		The next two numbers in the list, the 13th and 14th Mersenne primes, are much larger (corresponding to n=521 and n=607) and were both discovered the same day (January 30, 1952, around 22:00 PST and shortly before midnight) by Raphael Mitchel Robinson (1911-1995), at the dawn of the computer age.
	home.att.net /~numericana/answer/numbers.htm (7607 words)

	Math Horizons World Wide Web Treasure Hunt Results
		In addition, the number of twin primes -- primes that differ by 2 -- is close to the number of twin luckies.
		Luckies are featured in a similar conjecture, also unsolved: Every even number is the sum of two luckies.
		Notice that the sum of the prime factors of 714 is 2 + 3 + 7 + 17 = 29, and the sum of the prime factors of 715 is 5 + 11 + 13 = 29.
	www.maa.org /mathhorizons/Puzzles/Nov00-WWWtreasurehunt.htm (2877 words)

	Virtual Home of Paul Muljadi
		The alternating odd and even integer for i and j simulate a sieving process, which is normally used in generating prime sequences such as the lucky primes.
		A median number that is also prime is called a median prime.
		All median primes after 5 end with numbers 01, 13, 21, 41, 61, and 81.
	www.muljadi.org /Median.htm (220 words)

	Problem 18.- Pi as a concatenation of the smallest contiguous different primes
		The answer is "probably", because the next term in the sequence is at the moment only known to be a probable prime (it has now been tested to a very large number of bases).
		For comparison, the "general" prime record is currently (Sep 2002) a 5020-digit prime and took 13 weeks to prove with Primo.
		If the prime sequence is extended further then there will probably soon be a case where the first pi-decimal after a prime is 0.
	www.primepuzzles.net /problems/prob_018.htm (517 words)

	Science News Online - This Week - News Feature - 9/13/97 (Site not responding. Last check: 2007-10-20)
		One of the numbers that he happened to pick turned out to be a record-breaking prime -- the largest number yet identified that is evenly divisible only by itself and 1.
		Expressed in the form 2^p - 1, where the exponent p is itself a prime, Mersenne numbers have characteristics that make it relatively easy to determine whether a candidate is a prime.
		Because a program for testing primes constantly uses key parts of a microprocessor and stores and retrieves huge amounts of data, the chips can generate a greater than normal amount of heat, which sometimes causes failures.
	www.sciencenews.org /sn_arc97/9_13_97/fob1.htm (440 words)

	What's Special About This Number?
		is the largest number with the property that all smaller numbers relatively prime to it are prime.
		is the sum of the primes between its smallest and largest prime factor.
		is the smallest prime which is the sum of the cubes of the first few primes.
	www.stetson.edu /~efriedma/numbers.html (7473 words)

	The Math Forum - Math Library - Prime Numbers (Site not responding. Last check: 2007-10-20)
		Primes are the building blocks of the positive integers: every positive integer is a product of prime numbers in one and only one way, except...more>>
		Palindromic primes are whole numbers, evenly divisible only by themselves and 1, that also have the same sequence of digits read forward or backward...
		Exploring Pascal's triangle when the modulus is a prime; when the modulus is a power of a prime; and when the modulus has at least two different prime divisors.
	mathforum.org /library/topics/prime_numbers/?keyid=19270260&start_at=51&num_to_see=50 (1982 words)

	Index to Comic Art Collection: "Lucky Lady" to "Lucy's"
		Lucky Luke und der Großfürst / Zeichnungen, Morris ; Text, Goscinny.
		-- (J'ai Lu BD ; 166) -- Lucky Luke parody/tribute.
		Lucky Luke : Spécial 2 / textes et dessins de Morris.
	www.lib.msu.edu /comics/rri/lrri/lucky_l.htm (3897 words)

	Lucky Number -- from Wolfram MathWorld
		The first is the lucky numbers of Euler.
		Many asymptotic properties of the prime numbers are shared by the lucky numbers.
		, just as the prime number theorem, and the frequency of twin primes and twin lucky numbers are similar.
	mathworld.wolfram.com /LuckyNumber.html (280 words)

	Re: Lucky primes--third time's the charm? (Site not responding. Last check: 2007-10-20)
		You are in effect trying to search for a prime such that e's multiplicative inverse has a lot of 0's.
		But the only obvious attack would be to try to reproduce your prime-finding algorithm to find a p which divides the modulus n, and that is basically a sqrt(n) algorithm, which is far from the worst-case attack we face.
		Maybe you could choose a d such that d itself was 0-rich while ed happens not to be 0-rich; this might feel safer since p would have less of an arithmetical relation to a 0-rich number.
	cypherpunks.venona.com /date/1995/02/msg00430.html (310 words)

	New Page 1
		Thus since there is a finite number of primes there can only be a finite number of Fermat numbers (since Fermat numbers are relatively prime).
		-1 is prime, then a=2 and b is a prime.
		-1 is prime a=2, and b is a prime.
	www2.truman.edu /~c1199/math/Chapter5.htm (881 words)

	The Contest Center - Mathematical Puzzles
		A prime is an integer greater than 1 that cannot be evenly divided by another positive integer other than itself or 1.
		For example, given the primes 3, 7 and 13, the concatenations are 37, 73, 313, 133, 713, 137, 3713, 3137, 7313, 7133, 1337 and 1373, of which 6 are prime and 6 are composite.
		Using only the smaller numbers in sets of twin primes, form a 3x3 Magic Square (a 3x3 array of numbers where all of the rows and columns, and both of the main diagonals have the same sum).
	www.contestcen.com /prime.htm (1668 words)

	ARRI Newsletter
		We were lucky to reach Christian Almesberger, first camera assistant on "Perfume: The Story of a Murderer", who was on his way to a location in Spain while talking to us on his cell phone.
		I think it is great that all Master Primes have the same size and front diameter and that the focus and iris rings are in the same place.
		We have 11 Master Primes on the first unit, all focal lengths except the 65 mm, which is not ready yet, we were told, and the second unit also has some Master Primes.
	www.arri.com /news/newsletter/articles/09082005/almesberger.htm (752 words)

	Reaching new heights with new Mersenne prime!
		Mathematicians continue to study the distribution of the primes and especially the distribution of Mersenne primes.
		Perhaps the most important contribution of the project to mathematics is not the primes it finds, but showing that there are no other primes in between that have been missed (and this has happened before).
		For example, 53 is prime because it is not divisible 2, 3, 5 or 7.
	primes.utm.edu /notes/13466917 (918 words)

	Mersenne Newsletters Page
		Subject: Mersenne Prime Search Date: 24 Feb 96 21:18:21 EST Hello Mersenne Searchers, Enclosed is a newsletter to keep everyone up-to-date during the long, lonely search for Mersenne primes.
		If there are no Mersenne primes between M1398269 and M2976221, then the gap between the 35th and 36th Mersenne primes will be the 4th largest in percentage terms.
		In fact, in percentage terms, the gap between the 36th and 37th Mersenne primes is the smallest ever.
	www.garlic.com /~wedgingt/newsletters.html (7959 words)

	Re: Lucky primes & omlets on my face... (Site not responding. Last check: 2007-10-20)
		Re: Lucky primes and omlets on my face...
		> > This would only be true for prime p, but with RSA we are dealing with > composite moduli.
		Prev by thread: Re: Lucky primes and omlets on my face...
	cypherpunks.venona.com /date/1995/02/msg00110.html (160 words)

	CTK Exchange
		Removing 1 on the left and adding it to the remaining number is the same as subtracting 99 from the original number, right?
		If you wish 80 to be your lucky number, you have to insure that the number at stage c is bigger than 100.
		In your case, and if you insist there should be no limitation on the spectator's age, let it be 18.
	www.cut-the-knot.org /exchange/matterOfAge2.shtml (180 words)

	Dr. Dobb's \| Opening Disaster \| June 1, 2002
		In the second, there should be one prime, and it should be 2.
		In the third, there should be two primes: 2 and 3.
		In the last case, there should be 25 primes, the last of which is 97.
	www.ddj.com /184414876 (1153 words)

	Lucky Luke French comic books
		Lucky Luke - N 02 le Pied tendre
		Lucky Luke - N 14 Le fil qui chante
		Lucky Luke - N 32 Pont sur le Mississippi (le)
	www.europeanbook.com /luckyluke.html (156 words)

	Florence Ballard Fan Club
		Two of her neighbors, Eddie Kendricks and Paul Williams, sang in an upcoming group called the Primes (later to become the Temptations).
		They brought her to the,attention of their manager, Milton Jenkins, who was so impressed with the 14-year-old's voice that he asked her to perform as a soloist along with the Primes.
		Since groups were so popular in the late fifties, he suggested that Florence form a sister group to the Primes with himself as their manager.
	www.florenceballardfanclub.com /biography.htm (1866 words)

	LASTLY - nuwen.net
		It was to be dedicated to one purpose: performing Lucas-Lehmer tests on Mersenne numbers, as part of the Great Internet Mersenne Prime Search (GIMPS).
		Sadly, no Mersenne primes were found, but LASTLY did manage to eliminate 30 Mersenne numbers as candidates for primality.
		By a lucky coincidence, LASTLY was not affected by the Great Bug in the GIMPS program, when all computers that had done Lucas-Lehmer primality tests with a certain version of the program returned incorrect results which had to be redone.
	nuwen.net /lastly.html (512 words)

	Lucky, postal 2 - OpinionJournal - Extra (Site not responding. Last check: 2007-10-20)
		Lucky numbers share some properties with primes, such as asymptotic behaviour It is not known whether there are also infinitely many lucky primes:
		The aim of this addictive puzzle game is, to eliminate all the colorful balls rolling down the spiral tube, before they reach the skull.
		Lucky Strike Bait Works - manufacturers of: fishing hooks, tackle, nets, spinner baits, plugs, lead free sinkers, and famous half wave lure.
	postal-2.onlineinfosource.com /?q=postal-2-lucky (171 words)

	Reprolabels: Primes, Camshaft & WST Stickers - Transformers News and Reviews Daily - TFormers.com
		Especially Alternator/Binaltech Prime, makes him look sooo much better.
		Man I wish the PM Prime sticker sheet was a little cheaper, ill guess ill have to start saving now
		Looking at these, I can't believe I actually want to get Alt Drippy and Droopy (Prime and Camshaft), just to put these stickers on them.
	tformers.com /article.php?sid=6761 (1107 words)

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