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Topic: Palindromic prime

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Palindromic number

	Palindromic prime - Wikipedia, the free encyclopedia
		A palindromic prime is a prime number that is also a palindromic number.
		Palindromicity depends on the base of the numbering system and its writing conventions, while primality is independent of such concerns.
		It's possible that a triply palindromic prime in base 10 may be also be palindromic in another base, such as base 2, but it would be highly remarkable if it was also a triply palindromic prime in that base as well.
	en.wikipedia.org /wiki/Palindromic_prime (287 words)

	Palindromic number - Wikipedia, the free encyclopedia
		The term palindromic is derived from palindrome, which refers to a word like rotor that remains unchanged under reversal of its letters.
		the palindromic primes are 2, 3, 5, 7, 11, 101, 131, 151, … (sequence A002385 in OEIS)
		Although palindromic numbers are most often considered in the decimal system, the concept of palindromicity can be applied to the natural numbers in any numeral system.
	en.wikipedia.org /wiki/Palindromic_number (684 words)

	type
		Primes where all of the digits have holes; unholey primes do not have any digits with holes in them.
		A prime that must have a total even number of digits, and the digits in the first half of the prime must digger from the corrseponding digits of the second half, resulting in a coincidence ratio of 0.
		Primes that are named because they are usually expressed in their subscriptal notation.
	www.fortunecity.com /meltingpot/manchaca/799/type.html (541 words)

	Book Reviews
		Prime numbers are at the root of current computer security techniques involving cryptography such that the level of security is approximately equivalent the difficulty of factoring.
		It is not just about prime number records, but it is a great history of prime numbers with the personalities involved in the development of the field.
		The explanations of prime numbers of all kinds are supported by an extensive bibliography for each chapter and lots of proofs in the chapters.
	www.ieee-security.org /Cipher/BookReviews/970117.rb.bkrevs.html (665 words)

	MATHEWS: Palindromic Numbers (Site not responding. Last check: 2007-11-05)
		Palindromes are words or numbers which read the same forwards and backwards.
		Using the fact that the sum of the reciprocals of all palindromic numbers is convergent the sum of the reciprocals of the palindromic primes also converges to a constant.
		Because the first and last digit of a palindromic prime has to be odd, in the inequality the factor 9 can be improved to 1/1+1/3+1/7+1/9 = 1.587...
	www.wschnei.de /digit-related-numbers/palindromes.html (950 words)

	Prime Curios!: 181
		The 181-digit palindromic number made up of all 7s except for the center nut being 181 (7777...7718177...77777) is a palindromic prime with a palindromic prime decimal length.
		The first occurence of two consecutive primes which are both nontrivial (more than one digit) palindromes: 181, 191.
		The smallest palindromic prime number whose sum of digits is composite.
	primes.utm.edu /curios/page.php?short=181 (292 words)

	PalPrimePage 3
		Smallest palindromic prime that generates a palindromic prime pyramid of height n.
		Lengths of the palindromic primes from Honaker's sequence A053600.
		a(n+1) is the smallest palindromic prime with a(n) as a central substring.
	users.skynet.be /worldofnumbers/palprim3.htm (1543 words)

	Ivars Peterson's MathTrek - Primes, Palindromes, and Pyramids (Site not responding. Last check: 2007-11-05)
		In decimal notation, the sequence of palindromic primes begins with 2, 3, 5, 7, 11, 101, 131, 151, 181, 191, 313, 353, 373, 383, 727, 757, 787, 797, 919, 929, 10301, 10501, 10601, 11311, and so on.
		A palindromic prime pyramid is a sequence of primes in which each term is a palindrome with the previous term as its central digits.
		The idea of studying palindromic prime pyramids was first proposed by G.L. Honaker Jr., a teacher in Bristol, Va. Honaker later collaborated with mathematician and prime specialist Chris K. Caldwell of the University of Tennessee at Martin in a detailed investigation of these curious structures.
	www.maa.org /mathland/mathtrek_08_29_05.html (665 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 (7257 words)

	Palindromic Primes Assignment 3
		Smallest palindromes with exactly n distinct prime factors.
		Smallest palindromes with exactly n distinct palindromic prime factors.
		Palindromes divisible by the palindromic sum of their palindromic prime factors
	www.worldofnumbers.com /assign3.htm (563 words)

	Ivars Peterson's MathTrek - Palindromic Primes (Site not responding. Last check: 2007-11-05)
		Among these curiosities are the so-called palindromic primes--whole numbers, evenly divisible only by themselves and 1, that also have the same sequence of digits read forward or backward.
		In the realm of palindromic primes, 11 is the only one with an even number of digits.
		There are 15 palindromic primes consisting of three digits: 101, 131, 151, 181, 191, 313, 353, 373, 383, 727, 757, 787, 797, 919, and 929.
	www.maa.org /mathland/mathtrek_5_10_99.html (546 words)

	Pages of Shades - Legends, Myth & More...
		A very special kind of prime number [first mentioned to me by G. Honaker, Jr.] is a prime, p (that is, let's say, the kth prime number) in which the sum of the decimal digits of p is equal to the sum of the digits of k.
		The beastly palindromic prime number 16661 is such a number, since it is the 1928'th prime, and 1 + 6 + 6 + 6 + 1 = 1 + 9 + 2 + 8.
		Not only that, but it's a prime (p) for which the period length of the decimal expansion of its reciprocal (1/p) attains the maximum possible value of p-1.
	www.angelfire.com /realm/shades/demons/numberofthebeast.htm (2045 words)

	Fun with Primes (Site not responding. Last check: 2007-11-05)
		The largest known prime with only two different prime digits is 353535...3535353 (4157 digits).
		71828182828182817 is a palindromic prime formed from the decimal portion of e.
		Even better is that 179999999999999999917 is a prime where 17 9's are bounded by 17s.
	www.bath.ac.uk /~ma2crfs/funprimes.html (334 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 /~harveyh/primes.htm (1814 words)

	Supplement to "palindromic prime pyramids"
		In the paper "Palindromic prime pyramids" [HC2000] we discuss a type of pyramid first proposed by G. Honaker, Jr.
		Note that each row is a palindromic prime (a palprime) with the previous row as the central digit.
		For testing the primality of the numbers of the pyramid I used a "strong-pseudo prime" test and code, according to the pseudocode (Algorithm 6.1) described in the David M. Bressoud's book [Bressoud89] "Factorization and primality testing", Springer-Verlag, p.
	www.utm.edu /staff/caldwell/supplements (346 words)

	Palindromic prime (Site not responding. Last check: 2007-11-05)
		The first few palindromic primes in base 10 are
		It may be noticed that in the above list there are no 2- or 4- digit palindromic primes, except for 11.
		The first four non-Mersenne palindromic primes in binary are 5 (101), 17 (10001), 73 (1001001) and 107 (1101011).
	www.sciencedaily.com /encyclopedia/palindromic_prime (340 words)

	Puzzle 7.- Palindrome - Primes: 2 questions:
		is the first case of a prime palindrome (31513) obtained adding three consecutive primes, the central one of them being a palindrome prime also (10501), and asks if this will ever happen again?
		where there are 3 consecutive primes, the middle one palindromic, whose sum is palindromic prime.
		Let p be a palindrome where the first/last digit and all digits in even positions are in {0,1,2} and all other digits (odd internal positions) are in {7,8,9}.
	www.primepuzzles.net /puzzles/puzz_007.htm (492 words)

	The Prime Glossary: palindromic prime (Site not responding. Last check: 2007-11-05)
		A palindromic prime is simply a prime which is a palindrome.
		Obviously this depends on the base in which the number is written (for example, Mersenne primes are palindromic base 2).
		As an example of palindromic primes, here is a pyramid (list) of palindromic primes supplied by G.
	primes.utm.edu /glossary/page.php?sort=PalindromicPrime (95 words)

	Search:palindromic - OXiDE (Site not responding. Last check: 2007-11-05)
		palindromic number is a number (in some base b) that is the same when written forwards or backwards, i.e., of the...
		In the zoo of prime numbers, there are certain species that attract an inordinate amount of attent...
		A list of palindromes, which are words or phrases that read the same backwards or forwards.
	www.planetarabia.org (319 words)

	More Prime Patterns (Site not responding. Last check: 2007-11-05)
		If Q (2P+1) is itself a Sophie Germaine prime there are a total of 19 such triplets where each prime is palindromic.
		All 22 primes in the number range of 1 to 81 are attacked by the queen.
		A prime spiral arranged as a circle is thoroughly discussed and illustrated at Rom Sacks http://www.numberspiral.com/
	www.geocities.com /~harveyh/moreprimes.htm (1277 words)

	PalPrimePage 2 (Site not responding. Last check: 2007-11-05)
		Congrats to Jens (Kruse Andersen) and Harvey (Dubner) for 10^98689-42915192410^49340-1 98689 p138 04 Palindrome* It will be a long time before anyone finds a larger base-10 palindromic prime with a number of digits that is also a palindromic prime.
		Despite having a length that is not a prime nor a palindrome
		P, Q, R all have 727 digits, the number of digits is a palindromic prime.
	www.ping.be /~ping6758/palprim2.htm (1085 words)

	06/26/02: 131, the palindromic prime (Site not responding. Last check: 2007-11-05)
		is the 32nd prime and 1 + 3 + 1 = 3 + 2
		is the sum of three consecutive primes: 41 + 43 + 47
		is 131st Fibonacci number (1066340417491710595814572169) AND is the smallest Fibonacci prime which contains all the digits from 0 to 9.
	www.mrcranky.com /movies/juwannamann/115/131.html (80 words)

	(37*10^2883-73)/99 is palindromic prime
		This prime is a large palindromic prime with undulating prime digits.
		This number was likely proved to be prime while testing an ECPP algorithm implemented on a special purpose hardware based primality engine.
		It is likely that this prime was also proved prime by another test such as a Cyclotomy related test in that same year.
	www.isthe.com /chongo/tech/math/prime/37.html (229 words)

	Unusual Magic Cubes
		A reversible prime is a number, that when read in reverse, forms another prime.
		Interestingly, Carlos Rivera rediscovered this same prime magical square 30 years later, and published it as puzzle number 4 in his Prime Puzzles and Problems page in June 1998.
		As each number is to be a reversible prime, the cube would then consist of 96 distinct four-digit primes.
	members.shaw.ca /hdhcubes/cube_unusual.htm (4258 words)

	brightMystery: Cool Math Topic of the Week: Fun prime numbers (Site not responding. Last check: 2007-11-05)
		A prime number is a positive whole number larger than 1 which can be divided only by itself and the number 1.
		My favorite part of the Prime Pages is the Prime Curios section, where you can look at all sorts of different prime numbers that have all sorts of crazy properties.
		111181111: A palindromic prime, which is a prime number that is "spelled" the same forwards as backwards.
	www.brightmystery.net /movabletype/MovableType_blog/archives/2005/04/cool_math_topic_1.html (476 words)

	Phil Carmody found a prime (kottke.org) (Site not responding. Last check: 2007-11-05)
		Phil Carmody found a prime number which, when written in hexidecimal, forms a zip file that contains the code for decrypting DVDs.
		- 200 is the smallest number which cannot be turned into a prime number by modifying one of the digits.
		This entry is part of the kottke.org weblog, of which Book author to her publishing company: your lawsuit is not helping me or my book is the latest entry.
	www.kottke.org /01/03/phil-carmody-found-a-prime (230 words)

	About "Palindromic Primes" (Site not responding. Last check: 2007-11-05)
		Palindromic primes are whole numbers, evenly divisible only by themselves and 1, that also have the same sequence of digits read forward or backward...
		The current record for the largest known palindromic prime is held by Harvey Dubner, a retired electrical engineer in New Jersey.
		It's the sort of prime that reads the same forward, backward, upside down, and rotated...
	mathforum.org /library/view/9170.html (101 words)

	wu :: forums - Palindromic Prime with an even number of digits
		What if there exists a prime number with, say, 100 billion and 2 digits in it that is also palindromic.
		are the digits of the palindrome, they are all divisible by 11.
		In a palindrome of even length, the sum would be zero.
	www.ocf.berkeley.edu /~wwu/cgi-bin/yabb/YaBB.cgi?board=riddles_putnam;action=display;num=1110926518 (392 words)

	The Number of the Beast (Site not responding. Last check: 2007-11-05)
		The beastly palindromic prime number 16661 is such a number, since it is the 1928'th prime, and
		The sequence of palindromic primes begins 2, 3, 5, 7, 11, 101, 131, 151, 181, 191, 313, 353, etc. Taking the last two of these, we discover that 666 is the sum of two consecutive palindromic primes:
		If these 148 numbers (the first 148 digits of 1/149) are written as the top row of a 148x148 square grid, and then the digits of 2/149 as the second row, then 3/149 and so on, the result is a 148x148 pseudo-magic square, in which every row and column sums to 666.
	members.aol.com /s6sj7gt/mike666.htm (2634 words)

	StudyWorks! Online : Palindromic Primes (Site not responding. Last check: 2007-11-05)
		Palindromic numbers read the same backwards and forwards, like 2002.
		What is the only palindromic prime number with an even number of digits?
		(A prime number, like 7, is divisible only by itself and 1).
	www.studyworksonline.com /cda/content/article/0,,NAV3-39_SAR1660,00.shtml (68 words)

	Smoothly Undulating Palindromic Primes - SUPP's
		are numbers that are primes, palindromic in base 10, and the digits alternate,
		palindromic prime numbers with two distinct digits each, smaller than 843 digits long.
		Palindromic primes with just two distinct prime digits.
	www.worldofnumbers.com /undulat.htm (1133 words)

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