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	Supersingular prime
		In mathematics, a supersingular prime is a certain kind of prime number.
		It is also possible to define supersingular primes in a number-theoretic way using supersingular elliptic curves defined over the algebraic closure of the finite field GF(p) that have their j-invariant in GF(p).
		As is turns out, there are exactly fifteen supersingular primes: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 41, 47, 59, and 71.
	www.xasa.com /wiki/en/wikipedia/s/su/supersingular_prime.html (166 words)

	On the p-adic L-function of a modular form at a supersingular prime
		On the p-adic L-function of a modular form at a supersingular prime
		In this paper we study the two $p$-adic $L$-functions attached to a modular form $f=\sum a\sb nq\sp n$ at a supersingular prime $p$.
		When $a\sb p=0$, we are able to decompose both the sum and the difference of the two unbounded distributions attached to $f$ into a bounded measure and a distribution that accounts for all of the growth.
	www.projecteuclid.org /Dienst/UI/1.0/Summarize/euclid.dmj/1082744678 (734 words)

	59 (number) Encyclopedia (Site not responding. Last check: 2007-11-01)
		The next is sixty-one, with which it comprises a twin prime.
		59 is an irregular prime, a safe prime and a supersingular prime.
		It is an Eisenstein prime with no imaginary part and real part of the form 3n − 1.
	www.hallencyclopedia.com /topic/59_(number).html (497 words)

	Prime number (Site not responding. Last check: 2007-11-01)
		Prime ideals are an important tool and object of study in commutative algebra, algebraic number theory and algebraic geometry.
		The prime ideals of the ring of integers are the ideals (0), (2), (3), (5), (7), (11),...
		With this definition, the primes of the field Q of rational numbers are represented by the standard absolute value function (known as the "infinite prime") as well as by the p-adic valuations on Q, for every prime number p.
	www.free-download-soft.com /info/prime-numbers.html (2261 words)

	Prime_number
		The prime number theorem says that the proportion of primes less than x is asymptotic to 1/ln x (in other words, as x gets very large, the likelihood that a number less than x is prime is inversely proportional to the number of digits in x).
		From a mathematical viewpoint, it roughly states that the asymptotic distribution of primes (about 1/ log x of number less than x are primes, the prime number theorem) also holds for much shorter intervals of length about the square root of x (for intervals near x).
		A probable prime is an integer which, by virtue of having passed a certain test, is considered to be probably prime.
	www.plasmatvwholesaler.com /search.php?title=Prime_number (2847 words)

	Untitled Document
		There are two definitions of the supersingular primes: one group-theoretic, and the other number-theoretic.
		There are exactly 15 supersingular primes: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 41, 47, 59, and 71 (Sloane's
		The supersingular primes are exactly the set of primes that divide the
	users.skynet.be /fa956617/math/topics/SupersingularPrime.html (155 words)

	Supersingular prime - TheBestLinks.com - Algebraic closure, Iff, Mathematics, Natural number, ... (Site not responding. Last check: 2007-11-01)
		In mathematics, a supersingular prime is a certain kind of prime number.
		It is also possible to define supersingular primes in a number-theoretic way using supersingular elliptic curves defined over the algebraic closure of the finite field GF(p) that have their j-invariant in GF(p).
		As is turns out, there are exactly fifteen supersingular primes: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 41, 47, 59, and 71 (OEIS A002267 (http://www.research.att.com/projects/OEIS?Anum=A002267)).
	www.thebestlinks.com /Supersingular_prime.html (227 words)

	Articles - Prime number (Site not responding. Last check: 2007-11-01)
		Prime numbers are of fundamental importance in number theory.
		Prime numbers p where 2p + 1 is also prime are known as Sophie Germain primes.
		The largest prime gap with identified gap ends known as of 1 January 2005 has a length of 2254930 [1].
	www.estorea.com /articles/Prime_numbers (3131 words)

	Creation Functions (Site not responding. Last check: 2007-11-01)
		An ambient supersingular divisors module is specified by giving an integer N (the level) and a prime p (the characteristic).
		Equivalently, this is the free abelian group on the supersingular elliptic curves in characteristic p enhanced with level N structure.
		It is "cuspidal" in the sense that X tensor Q is isomorphic as a Hecke module to the space S_2(Gamma_0(Np);Q)^p-new of p-new cuspforms with Fourier coefficients in Q. Explicitly, the cuspidal subspace is the subspace of elements such that the sum of the coefficients is 0 (i.e., the subspace of divisors of degree 0).
	cso.ulb.ac.be /~dleemans/magma/text1268.htm (678 words)

	Read about Supersingular prime at WorldVillage Encyclopedia. Research Supersingular prime and learn about Supersingular ... (Site not responding. Last check: 2007-11-01)
		In mathematics, a supersingular prime is a certain kind of
		As is turns out, there are exactly fifteen supersingular primes: 2, 3, 5,
		It can also be shown that the supersingular primes are exactly the prime factors of the group order of the Monster group M.
	encyclopedia.worldvillage.com /s/b/Supersingular_prime (157 words)

	Creation Functions
		Equivalently, this is the free abelian group on the isomorphism classes of supersingular elliptic curves in characteristic p enhanced with level N structure.
		So we verify that the supersingular cuspidal space of level 11 is of dimension 1 --- precisely that associated to the isogeny class of the elliptic curve of level 11.
		The kernel of I on M. This is the subspace of M obtained by intersecting the kernels of the operators f_i(T_(p_i)), where I is a sequence [< p_1, f_1(x) >,..., < p_n, f_n(x) >] of pairs consisting of a prime number and a polynomial.
	www.umich.edu /~gpcc/scs/magma/text1129.htm (657 words)

	Supersingular prime - Encyclopedia Glossary Meaning Explanation Supersingular prime (Site not responding. Last check: 2007-11-01)
		Supersingular prime - Encyclopedia Glossary Meaning Explanation Supersingular prime.
		Then p is supersingular means by definition that the genus of X
		As is turns out, there are exactly fifteen supersingular primes: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 41, 47, 59, and 71.
	www.encyclopedia-glossary.com /en/Supersingular-prime.html (215 words)

	Prime Curios!: 71
		A 71-digit prime is formed by intertwining the even (from 2 to 40) and the odd (from 1 to 39) numbers (214365...374039).
		The most common final digits of a Mersenne Prime (among all known ones) is a tie between the prime 71 and 51 (6 occurrences each).
		71 is the largest of the supersingular primes, i.e., the set of primes that divide the group order of the Monster group.
	primes.utm.edu /curios/page.php/71.html (458 words)

	Public key cryptosystem with an elliptic curve - Patent 5272755
		Proof of p.sub.1 and p.sub.2 being prime numbers is given from the fact that p.sub.1 and p.sub.2 are factors of a power of 2 plus 1, and therefore, that they are represented in abnormal forms, for instance, 2.sup.191 +1 and 2.sup.251 +1 are represented as 2.multidot.191.multidot.m+1 and 2.multidot.251.multidot.m+1, respectively.
		Let p be the greatest prime factor of E.sub.i (GF(2.sup.m)), and let t be a sufficiently large positive integer, so that 2.sup.mk -1 do not have p as a prime factor, where k is a positive integer smaller than or equal to t.
		Let p be a large prime and m be expressed by m=p'k (k is an integer prime to p, t is a positive integer).
	www.freepatentsonline.com /5272755.html (8057 words)

	Articles - 59 (number) (Site not responding. Last check: 2007-11-01)
		The next is sixty-one, with which it comprises a twin prime.
		59 is an irregular prime, a safe prime and a supersingular prime.
		It is an Eisenstein prime with no imaginary part and real part of the form 3n âˆ’ 1.
	www.winacea.com /articles/59_(number) (247 words)

	Articles - 71 (number) (Site not responding. Last check: 2007-11-01)
		The next is 73, with which it composes a twin prime.
		It is also a permutable prime with 17.
		If we add up the primes less than 71 (2 through 67), we get 568, which is divisible by 71, 8 times.
	www.landize.com /articles/71_(number) (280 words)

	Introduction
		A divisor on the supersingular points of X_0(1) in characteristic p is a finite formal linear combination of supersingular j-invariants j in (F)_(p^2).
		The supersingular points of X_0(N)/(F)_p correspond to singularities of the special fiber of a minimal model of X_0(Np) at p.
		When using Brandt modules to compute the module of supersingular divisor in Magma, no facility is currently provided for describing the divisors in terms of supersingular elliptic curves.
	www.math.lsu.edu /magma/text1289.htm (562 words)

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