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Specific class of fifteen prime numbers
In moonshine theory, a supersingular prime is a prime number that divides the order of the Monster group M {\displaystyle M} , which is the largest sporadic
Supersingular prime (moonshine theory)
Supersingular_prime_(moonshine_theory)
Prime number with a certain relationship to an elliptic curve
In algebraic number theory, a supersingular prime for a given elliptic curve is a prime number with a certain relationship to that curve. If the curve
Supersingular prime (algebraic number theory)
Supersingular_prime_(algebraic_number_theory)
Mathematical concept
In arithmetic geometry, supersingular elliptic curves form a certain class of elliptic curves over a field of characteristic p > 0 {\displaystyle p>0}
Supersingular_elliptic_curve
Topics referred to by the same term
a supersingular prime is a prime number satisfying one of the following concepts: Supersingular prime (algebraic number theory) Supersingular prime (moonshine
Supersingular_prime
859, 877, 919, 967, 991 (OEIS: A006450) There are exactly fifteen supersingular primes: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 41, 47, 59, 71 (OEIS: A002267)
List_of_prime_numbers
Natural number
a safe prime, a sexy prime, and a supersingular prime. The next prime number is sixty-one, with which it comprises a twin prime. There are 59 stellations
59_(number)
Natural number
Ramanujan prime, a harmonic prime, a good prime, a Newman–Shanks–Williams prime, and the 12th supersingular prime. It is the smallest Sophie Germain prime to
41_(number)
Post-quantum cryptographic algorithm
Supersingular isogeny Diffie–Hellman key exchange (SIDH or SIKE) was an insecure proposal for a post-quantum cryptographic algorithm to establish a secret
Supersingular isogeny key exchange
Supersingular_isogeny_key_exchange
Natural number
safe prime, a Thabit prime, a regular prime, a cluster prime, an isolated prime, a Ramanujan prime, and a Higgs prime. 47 is also a supersingular prime. It
47_(number)
Natural number
with noncompact unbounded fundamental polyhedra. 29 is the tenth supersingular prime. In this sequence, 29 is the seventeenth indexed member, where the
29_(number)
Natural number
largest number which occurs as a prime factor of an order of a sporadic simple group, the largest (15th) supersingular prime. F 14 ( 71 ) = 71 16384 + 1 2
71_(number)
Natural number
generate a magic constant of 81 = 92. 19 is a supersingular prime, a member in the sequence of fifteen such primes that divide the order of the Friendly Giant
19_(number)
Prime number p where p+2 is prime or semiprime
non-Chen primes are 43, 61, 73, 79, 97, 103, 151, 163, 173, 193, 223, 229, 241, ... (sequence A102540 in the OEIS). All of the supersingular primes are Chen
Chen_prime
Natural number
n+2} mirror facets, with the lowest belonging to the third. 17 is a supersingular prime, because it divides the order of the Monster group. If the Tits group
17_(number)
Prime number of the form 2^n – 1
In mathematics, a Mersenne prime is a prime number that is one less than a power of two. That is, it is a prime number of the form Mn = 2n − 1 for some
Mersenne_prime
Natural number
first 15 colossally abundant numbers. There are 15 supersingular primes. There are 15 truncatable primes that are both right-truncatable and left-truncatable:
15_(number)
Natural number
2023-03-02. Sloane, N. J. A. (ed.). "Sequence A002267 (The 15 supersingular primes: primes dividing order of Monster simple group.)". The On-Line Encyclopedia
193_(number)
Natural number
37. In moonshine theory, whereas all p ⩾ 73 are non-supersingular primes, the smallest such prime is 37. 37 is the sixth floor of imaginary parts of non-trivial
37_(number)
Prime such that p^2 divides 2^(p-1)-1
In number theory, a Wieferich prime is a prime number p such that p2 divides 2p − 1 − 1, therefore connecting these primes with Fermat's little theorem
Wieferich_prime
Mathematical concept
In mathematics, a supersingular variety is (usually) a smooth projective variety in nonzero characteristic such that for all n the slopes of the Newton
Supersingular_variety
Sporadic simple group
Monstrous Moonshine is in one sentence, it is the voice of God." Supersingular prime, the prime numbers that divide the order of the monster Bimonster group
Monster_group
Natural number
composite factors (22021 = 192 × 61) were prime. 61 is the largest prime number (less than the largest supersingular prime, 71) that does not divide the order
61_(number)
Cryptography secured against quantum computers
in the supersingular isogeny Diffie–Hellman (SIDH) method, De Feo, Jao and Plut recommend using a supersingular curve modulo of a 768-bit prime. If one
Post-quantum_cryptography
Monster and modular connection
became known as "The Jack Daniel's Problem". These 15 primes are now known as the supersingular primes, not to be confused with the use of the same phrase
Monstrous_moonshine
Prime number congruent to 1 mod 4
A Pythagorean prime is a prime number of the form 4 n + 1 {\displaystyle 4n+1} . Pythagorean primes are exactly the odd prime numbers that are the sum
Pythagorean_prime
Prime number that is product of first n primes ± 1
mathematics, a primorial prime is a prime number of the form pn# ± 1, where pn# is the primorial of pn (i.e. the product of the first n primes). Primality tests
Primorial_prime
Class of expander graphs arising in computational number theory
choosing a large prime number p {\displaystyle p} and a small prime number ℓ {\displaystyle \ell } , and considering the class of all supersingular elliptic curves
Supersingular_isogeny_graph
American mathematician (born 1966)
proved that an elliptic curve over the rational numbers is supersingular at infinitely many primes. In 1988, he found a counterexample to Euler's sum of powers
Noam_Elkies
Prime number of the form that allows fast modular reduction
In mathematics, a Solinas prime, or generalized Mersenne prime, is a prime number that has the form f ( 2 m ) {\displaystyle f(2^{m})} , where f ( x )
Solinas_prime
Prime number of the form (2ᵖ+1)/3
theory, a Wagstaff prime is a prime number of the form 2 p + 1 3 {\displaystyle {{2^{p}+1} \over 3}} where p is an odd prime. Wagstaff primes are named after
Wagstaff_prime
cyclotomic field. Lang and Trotter's conjecture on supersingular primes that the number of supersingular primes less than a constant X {\displaystyle X} is within
List of unsolved problems in mathematics
List_of_unsolved_problems_in_mathematics
Orientation-preserving mapping class group of the torus
divides the order of the monster group, or equivalently, if p is a supersingular prime. One important subset of the modular group is the dyadic monoid,
Modular_group
Type of prime number
In number theory, a Wilson prime is a prime number p {\displaystyle p} such that p 2 {\displaystyle p^{2}} divides ( p − 1 ) ! + 1 {\displaystyle (p-1)
Wilson_prime
Online database of integer sequences
"fini". One example of a finite sequence given in full is that of the supersingular primes A002267, of which there are precisely fifteen. hard – The terms of
On-Line Encyclopedia of Integer Sequences
On-Line_Encyclopedia_of_Integer_Sequences
Type of prime number
A cuban prime is a prime number that is also a solution to one of two different specific equations involving differences between third powers of two integers
Cuban_prime
Prime number of the form 2^u × 3^v + 1
In number theory, a Pierpont prime is a prime number of the form 2 u ⋅ 3 v + 1 {\displaystyle 2^{u}\cdot 3^{v}+1\,} for some nonnegative integers u and
Pierpont_prime
Number of form 2^(2^p-1)-1 with prime exponent
number that is prime is called a double Mersenne prime. Since a Mersenne number Mp can be prime only if p is prime, (see Mersenne prime for a proof), a
Double_Mersenne_number
called X0+(N), and for N prime this has genus zero only for a finite list of primes, called supersingular primes, which are the primes that divide the order
Fricke_involution
Sporadic simple group
outer automorphism group are both trivial. Since 37 and 43 are not supersingular primes, J4 cannot be a subquotient of the monster group. Thus it is one
Janko_group_J4
Prime number one less or more than a factorial
factorial prime is a prime number that is one less or one more than a factorial (all factorials greater than 1 are even). The first 10 factorial primes (for
Factorial_prime
Approach to public-key cryptography
states that CNSA 1.0 compliance remains required during the transition. Supersingular Isogeny Diffie–Hellman Key Exchange was proposed as a post-quantum form
Elliptic-curve_cryptography
American mathematician
elliptic curves and modular curves. His 1975 observation connecting supersingular primes to the monster group is widely regarded as the earliest hint of monstrous
Andrew_Ogg
Result on density of prime numbers
that for any integer n > 3 {\displaystyle n>3} , there exists at least one prime number p {\displaystyle p} with n < p < 2 n − 2. {\displaystyle n<p<2n-2
Bertrand's_postulate
Algebraic variety
31, 41, 47, 59 or 71, and these are precisely supersingular primes in moonshine theory, i.e. the prime factors of the order of the monster group. The
Modular_curve
Positive integer of the form (2^(2^n))+1
If 2k + 1 is prime and k > 0, then k itself must be a power of 2, so 2k + 1 is a Fermat number; such primes are called Fermat primes. As of 2026[update]
Fermat_number
Number of the form (n * 2^n) - 1
infinitely many Woodall primes? More unsolved problems in mathematics Woodall numbers that are also prime numbers are called Woodall primes; the first few exponents
Woodall_number
Special type of prime number
In number theory, a Wolstenholme prime is a special type of prime number satisfying a stronger version of Wolstenholme's theorem. Wolstenholme's theorem
Wolstenholme_prime
2011 soundtrack album by Mike Patton
The Solitude of Prime Numbers (2011) is a soundtrack album by Mike Patton for the film The Solitude of Prime Numbers, directed by Saverio Costanzo. The
The Solitude of Prime Numbers (soundtrack)
The_Solitude_of_Prime_Numbers_(soundtrack)
quartic Modular curve Modular equation Modular function Modular group Supersingular primes Fermat curve Bézout's theorem Brill–Noether theory Genus (mathematics)
List of algebraic geometry topics
List_of_algebraic_geometry_topics
Integer of the form 3 × 2^n – 1 for non-negative n
"10" followed by n 1s. The first few Thabit numbers that are prime (Thabit primes or 321 primes): 2, 5, 11, 23, 47, 191, 383, 6143, 786431, 51539607551, 824633720831
Thabit_number
Sporadic simple group
outer automorphism group are both trivial. Since 37 and 67 are not supersingular primes, the Lyons group cannot be a subquotient of the monster group. Thus
Lyons_group
Method of exchanging cryptographic keys
n. Variants using hyperelliptic curves have also been proposed. The supersingular isogeny key exchange is a Diffie–Hellman variant that was designed to
Diffie–Hellman_key_exchange
Project by NIST to standardize post-quantum cryptography
post-quantum signature". Mqdss.org. Retrieved 31 January 2019. "SIKE – Supersingular Isogeny Key Encapsulation". Sike.org. Retrieved 31 January 2019. "Picnic
NIST Post-Quantum Cryptography Standardization
NIST_Post-Quantum_Cryptography_Standardization
Mathematical surface
In algebraic geometry, a supersingular K3 surface is a K3 surface over a field k of characteristic p > 0 such that the slopes of Frobenius on the crystalline
Supersingular_K3_surface
Number of the form x^y + y^x
Leyland numbers (so we have 1 < y ≤ x). A Leyland prime is a Leyland number that is prime. The first such primes are: 17, 593, 32993, 2097593, 8589935681, 59604644783353249
Leyland_number
Mathematical concept
Cullen primes at The Prime Pages. The Prime Glossary: Cullen number at The Prime Pages. Chris Caldwell, The Top Twenty: Generalized Cullen at The Prime Pages
Cullen_number
Dutch mathematician
Geometry, Oslo 1970, Wolters-Noordhoff 1972 with Ke-Zheng Li: Moduli of supersingular abelian varieties, Springer 1998 as editor with Steenbrink and van der
Frans_Oort
possibilities for the matrix H are: H is zero, Hasse invariant 0, p-rank 0, the supersingular case; or H non-zero, Hasse invariant 1, p-rank 1, the ordinary case
Hasse–Witt_matrix
Product of prime numbers, plus one
prime numbers). They are named after the ancient Greek mathematician Euclid, in connection with Euclid's theorem that there are infinitely many prime
Euclid_number
Spectral graph theory concept
construction holds whenever p {\displaystyle p} is a prime power. Arnold Pizer proved that the supersingular isogeny graphs are Ramanujan, although they tend
Ramanujan_graph
Weil cohomology theory for schemes X over a base field k
The classic reason (due to Serre) is that if X {\displaystyle X} is a supersingular elliptic curve, then its endomorphism ring is a maximal order in a quaternion
Crystalline_cohomology
Assumption used in cryptographic systems
log 2 ( p ) {\displaystyle \log ^{2}(p)} ), a class which includes supersingular elliptic curves. This is because the Weil pairing or Tate pairing can
Decisional Diffie–Hellman assumption
Decisional_Diffie–Hellman_assumption
Technique in cryptography
previous bound for successfully computing a discrete logarithm on a supersingular elliptic curve from 676 bits to 923 bits. In 2016, the Extended Tower
Pairing-based_cryptography
Probabilistic algorithm for computing discrete logarithms
elliptic curve groups. However: For special kinds of curves (so called supersingular elliptic curves) there are specialized algorithms for solving the problem
Index_calculus_algorithm
On generating functions from counting points on algebraic varieties over finite fields
cannot be the rational numbers. To see this consider the case of a supersingular elliptic curve over a finite field of characteristic p. The endomorphism
Weil_conjectures
Type of mathematical object
the curve is ordinary) or one connected component (if the curve is supersingular). If we consider a family of elliptic curves, the p-torsion forms a
Group_scheme
Mathematical terminology
related to the representations of elliptic curves with ordinary (non-supersingular) reduction. More precisely, they are 2-dimensional representations that
Galois_representation
Algebraic curve in mathematics
exchange (ECDH) Elliptic curve digital signature algorithm (ECDSA) Supersingular isogeny key exchange Elliptic curve primality proving Lenstra elliptic-curve
Elliptic_curve
Best results achieved to date
Thorsten Kleinjung, and Jens Zumbrägel. "Breaking `128-Bit Secure’ Supersingular Binary Curves (or How to Solve Discrete Logarithms in F 2 4 ⋅ 1223 {\displaystyle
Discrete_logarithm_records
Graduate-level textbooks in mathematics
Theory Stanley Chang, Shmuel Weinberger 2021-01-26 442 9780691160498 212 Supersingular p-adic L-functions, Maass-Shimura Operators and Waldspurger Formulas
Annals_of_Mathematics_Studies
Mathematical classification of surfaces
there are some extra families of Enriques surfaces called singular and supersingular Enriques surfaces; see the article on Enriques surfaces for details
Enriques–Kodaira classification
Enriques–Kodaira_classification
Substitution cipher • Substitution–permutation network • Superencryption • Supersingular isogeny key exchange • Swedish National Defence Radio Establishment
Index of cryptography articles
Index_of_cryptography_articles
Brazilian-American cryptographer (born 1965)
Ó'hÉigeartaigh, Colm; Scott, Mike (2007). "Efficient pairing computation on supersingular Abelian varieties". Designs, Codes and Cryptography. 42 (3): 239–271
Paulo_S._L._M._Barreto
E} is a supersingular elliptic curve, such as E : y 2 = x 3 − 3 x {\displaystyle \textstyle E:y^{2}=x^{3}-3x} (over a finite field of prime order p {\displaystyle
Sakai–Kasahara_scheme
rational curve through every k-point. (The Kummer variety of any non-supersingular abelian surface over Fp with p odd has these properties.) It is not
Ruled_variety
SUPERSINGULAR PRIME
SUPERSINGULAR PRIME
Girl/Female
Arabic, Muslim
Best Selected; The Best Part; Elite; Top; Prime; Flower
Boy/Male
Arabic, Muslim
Prime Minister
Boy/Male
Indian, Tamil
Important; Prime
Surname or Lastname
English
English : variant of Prime, or from an Old English personal name Preng.
Surname or Lastname
German
German : of uncertain origin; possibly from the Latin personal name Primus (‘the first’), borne by several saints; or one composed with a Germanic word meaning ‘to prick or stab’; or from a personal name of Slavic origin Primm, from prēmu ‘right’.French : from a personal name (from Latin Primus).French : nickname from Old French prim ‘first’, possibly given to the eldest child in a family, or alternatively a nickname from Old French and Occitan prim ‘shrewd’, ‘clever’, ‘artful’, ‘sly’.Dutch : variant of Priem.English : variant of Prime.Some of the Prim families in VT descend from a Simon Laval dit Printemps, who was known in English-speaking areas as Seymour Prim.
Girl/Female
Persian American
Child of light. Famous Bearer: Margaret Thatcher, former Prime Minister of the United Kingdom.
Surname or Lastname
English
English : unexplained.Serbian : unexplained.
Boy/Male
Muslim
Prime minister
Boy/Male
Arabic, Muslim, Sindhi
Start; Forefront; Dawn; Bosom; Prime; The Highest Part; Heart
Boy/Male
Arabic, Muslim, Pashtun
Prime Chief
Girl/Female
English American Israeli
The precious metal.. Late prime minister of Israel Golda Meir.
Surname or Lastname
English
English : from a Middle English personal name or nickname. The personal name existed in Old English, and is probably derived from Old English prim ‘early morning’ (from Latin primus ‘first’, used as the name of one of the canonical hours). The surname may be derived from this word as a Middle English nickname in the sense ‘fine’, ‘excellent’.French : feminine form of Prim 3.Dutch : variant of Priem.Probably an Americanized spelling of German Preim, a topographic name (of Slavic origin), perhaps from a river near Hannover; or of Preime, a variant of Primus.
Girl/Female
Persian American
Child of light. Famous Bearer: Margaret Thatcher, former Prime Minister of the United Kingdom.
Girl/Female
German, Hebrew, Hindu, Indian, Kannada, Sanskrit
Adornment; Jewel; The First; Primeval; Daughter of Earth; My Ornament; My Witness; Ornament
Girl/Female
Persian American English Greek
Child of light. Famous Bearer: Margaret Thatcher, former Prime Minister of the United Kingdom.
Girl/Female
Australian, Christian, Danish, Greek, Latin, Swedish
Prime of Life; Youth; Goddess of Youth and Cup-bearer to the Gods; Granddaughter of Zeus and Hera
Girl/Female
Afghan, Arabic, German, Hindu, Indian, Iranian, Muslim, Parsi, Sindhi, Turkish
Spring Season; Prime of Life; Bloom of Youth
Boy/Male
Spanish
Born first.
Boy/Male
Indian
Prime
Boy/Male
Hindu, Indian
Chief; Prime
SUPERSINGULAR PRIME
SUPERSINGULAR PRIME
SUPERSINGULAR PRIME
SUPERSINGULAR PRIME
SUPERSINGULAR PRIME
SUPERSINGULAR PRIME
SUPERSINGULAR PRIME