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Problem Any problem in number theory (m,k)-perfect numbers A binomial coefficient sum A binomial coefficient summation A conjecture by Margulis on matrix groups A GCD-Driven Sequence with Universal Jumps a(0) = 1, a(n) = a(n-1)a(n-1) + 2 a(n) = (smallest prime > n^2) - n^2 a(n) = 2^(2^n) a(n) = 3a(n-1) + a(n-2) - 3a(n-3) a(n) = lcm1,2,…,n/denom(H(n)) a(n) = the number of values of k <= 10^n such that √(k(k+1)(k+2)(k+3)+1) is prime a(n) = Σ_j=1^n (3^j + (-2)^j) a(n) = Σ_k=0^n C(2k, k)^3 a(n) is the integer whose decimal digits are the first n+1 decimal digits of π abc conjecture Agoh-Giuga conjecture Agrawal's conjecture Alternating sum of signs of powers of 3/2 Amicable numbers An Arithmetic Sum Associated with the Classical Theta Function Andrica's conjecture Apéry numbers Are prime numbers among sums of prime numbers distributed as frac n2ln(n)? Array read by upward antidiagonals Artin's conjecture on primitive roots Ascending descending base exponent transform of 2^n Ascending descending base exponent transform of factorials Ascending descending base exponent transform of squares Asymptotic density of powerful numbers Asymptotic Dobrowolski constant for Lehmer’s problem Balanced prime conjecture Bateman-Horn Conjecture Beal conjecture Ben Green's Open Problem 2 Ben Green's Open Problem 45 Ben Green's Open Problem 46 Ben Green's Open Problem 60 Ben Green's Open Problem 61 Ben Green's Open Problem 62 Ben Green's Open Problem 66 Ben Green's Open Problem 82 Betrothed numbers Binary representation of primes that divide a number, in decimal Bounded prime gap constant Brocard's Conjecture Brun's Constant Büchi's problem Bugeaud Collection of Conjectures and Open Questions: Confined Powers of Non-Pisot Numbers Bugeaud Collection of Conjectures and Open Questions: Fractional Parts of Powers Bugeaud Collection of Conjectures and Open Questions: Mahler's Z-numbers Bugeaud Collection of Conjectures and Open Questions: p-adic Littlewood Conjecture Bugeaud Collection of Conjectures and Open Questions: Pisot orbits on the Cantor set Bunyakovsky conjecture Burgess-quality subconvexity exponent for Dirichlet L-functions Can a prime p satisfy 2^p-1 ≡ 1 pmodp^2 and 3^p-1 ≡ 1 pmodp^2? Carmichael's totient function conjecture Catalan-Mersenne numbers Catalan's conjecture and related Diophantine equations Central binomial sum a(n) = Σ_k=0^n (-4)^k C(n, k)^2 C(n-k, k)^2 Central binomial sum a(n) = Σ_k=0^n C(n, k)^2 C(n-k, k)^2 (-16)^k Central trinomial coefficients Chua's Euclidean prime sequence Class number problem for real quadratic fields Classical zero-free region constant Coefficients of Π_k>0 (1 - x^k/k!) Collatz step differences Concatenation of the next n numbers Congruent Number Conjectures about Mersenne primes Conjectures associated with A038552 Conjectures associated with A063880 Conjectures associated with A067720 Conjectures associated with A100474 Conjectures associated with A100800 Conjectures associated with A101779 Conjectures associated with A105210 Conjectures associated with A109227 Conjectures associated with A109671 Conjectures associated with A109845 Conjectures associated with A109905 Conjectures associated with A109908 Conjectures associated with A109909 Conjectures associated with A110854 Cuban Primes Cunningham chains — Jones's conjecture Decimal encoding of the prime factorization of n Denominator of sum of reciprocals of divisors Denominator of Σ_k=1^n k^μ(k) Denominators of coefficients in Stirling's expansion for log(Γ(z)) Determinant of Hankel matrix of the first 2n-1 prime numbers Determinant of matrix with entries indicating primality of i^2 + j^2 Determinants of 2 X 2 matrices of non-overlapping blocks of 4 consecutive primes Dickson's conjecture Difference between first odd semiprime > 2^n and 2^n Difference of digit sums in base 3 and base 2 Digital sum of the Fermat number 2^2^n + 1 Diophantine m-tuples Dirichlet divisor problem exponent Divisibility of 2^n + 1 by n Do odd perfect numbers exist? Dubner's conjecture Elliott-Halberstam level-of-distribution exponent Elliott–Halberstam conjecture Equidistributed Sequences Erdős Problem #1002 Erdős Problem #1003 Erdős Problem #1004 Erdős Problem #1049 Erdős Problem #1052 Erdős Problem #1054 Erdős Problem #1055 Erdős Problem #1056 Erdős Problem #1057 Erdős Problem #1059 Erdős Problem #1060 Erdős Problem #1061 Erdős Problem #1062 Erdős Problem #1063 Erdős Problem #1065 Erdős Problem #1072 Erdős Problem #1073 Erdős Problem #1074 Erdős Problem #1094 Erdős Problem #11 Erdős Problem #1101 Erdős Problem #1106 Erdős Problem #1107 Erdős Problem #1108 Erdős Problem #1113 Erdős Problem #1135 Erdős Problem #1137 Erdős Problem #1139 Erdős Problem #1142 Erdős Problem #1146 Erdős Problem #12 Erdős Problem #1201 Erdős Problem #1203 Erdős Problem #1209 Erdős Problem #1210 Erdős Problem #1212 Erdős Problem #124 Erdős Problem #137 Erdős Problem #138 Erdős Problem #14 Erdős Problem #142 Erdős Problem #143 Erdős Problem #145 Erdős Problem #148 Erdős Problem #15 Erdős Problem #168 Erdős Problem #17 Erdős Problem #18 Erdős Problem #208 Erdős Problem #233 Erdős Problem #234 Erdős Problem #238 Erdős Problem #244 Erdős Problem #247 Erdős Problem #249 Erdős Problem #25 Erdős Problem #251 Erdős Problem #252 Erdős Problem #257 Erdős Problem #261 Erdős Problem #263 Erdős Problem #264 Erdős Problem #276 Erdős Problem #279 Erdős Problem #28 Erdős Problem #287 Erdős Problem #288 Erdős Problem #289 Erdős Problem #291 Erdős Problem #3 Erdős Problem #30 Erdős Problem #302 Erdős Problem #304 Erdős Problem #306 Erdős Problem #307 Erdős Problem #313 Erdős Problem #317 Erdős Problem #32 Erdős Problem #322 Erdős Problem #323 Erdős Problem #324 Erdős Problem #325 Erdős Problem #33 Erdős Problem #332 Erdős Problem #348 Erdős Problem #349 Erdős Problem #354 Erdős Problem #357 Erdős Problem #359 Erdős Problem #361 Erdős Problem #364 Erdős Problem #366 Erdős Problem #367 Erdős Problem #371 Erdős Problem #373 Erdős Problem #375 Erdős Problem #376 Erdős Problem #377 Erdős Problem #383 Erdős Problem #385 Erdős Problem #386 Erdős Problem #389 Erdős Problem #39 Erdős Problem #390 Erdős Problem #396 Erdős Problem #398 Erdős Problem #40 Erdős Problem #400 Erdős Problem #406 Erdős Problem #409 Erdős Problem #41 Erdős Problem #410 Erdős Problem #412 Erdős Problem #413 Erdős Problem #414 Erdős Problem #416 Erdős Problem #417 Erdős Problem #422 Erdős Problem #428 Erdős Problem #431 Erdős Problem #445 Erdős Problem #450 Erdős Problem #452 Erdős Problem #454 Erdős Problem #455 Erdős Problem #456 Erdős Problem #458 Erdős Problem #462 Erdős Problem #463 Erdős Problem #470 Erdős Problem #478 Erdős Problem #479 Erdős Problem #495 Erdős Problem #5 Erdős Problem #50 Erdős Problem #51 Erdős Problem #510 Erdős Problem #52 Erdős Problem #536 Erdős Problem #538 Erdős Problem #647 Erdős Problem #66 Erdős Problem #672 Erdős Problem #677 Erdős Problem #68 Erdős Problem #680 Erdős Problem #681 Erdős Problem #683 Erdős Problem #686 Erdős Problem #688 Erdős Problem #689 Erdős Problem #695 Erdős Problem #699 Erdős Problem #7 Erdős Problem #700 Erdős Problem #726 Erdős Problem #727 Erdős Problem #749 Erdős Problem #770 Erdős Problem #773 Erdős Problem #779 Erdős Problem #786 Erdős Problem #821 Erdős Problem #826 Erdős Problem #828 Erdős Problem #829 Erdős Problem #830 Erdős Problem #839 Erdős Problem #849 Erdős Problem #850 Erdős Problem #853 Erdős Problem #855 Erdős Problem #859 Erdős Problem #873 Erdős Problem #885 Erdős Problem #886 Erdős Problem #887 Erdős Problem #889 Erdős Problem #890 Erdős Problem #891 Erdős Problem #912 Erdős Problem #913 Erdős Problem #930 Erdős Problem #931 Erdős Problem #932 Erdős Problem #933 Erdős Problem #938 Erdős Problem #939 Erdős Problem #940 Erdős Problem #942 Erdős Problem #943 Erdős Problem #944 Erdős Problem #945 Erdős Problem #950 Erdős Problem #951 Erdős Problem #952 Erdős Problem #955 Erdős Problem #961 Erdős Problem #962 Erdős Problem #968 Erdős Problem #970 Erdős Problem #971 Erdős Problem #972 Erdős Problem #975 Erdős Problem #978 Erdős Problem #979 Erdős Problem #985 Erdős Problem #995 Erdős squarefree problem Essential minimum of the Zhang-Zagier height Euclid Numbers conjecture Euclid-Mullin sequence Euler's sum of powers conjecture Expansion of (1 - x)/(1 - 2 x + 3 x^2) Exponent for bounded gaps between many primes Factorial distance to nearest square Factorial primes Factoring N! into N numbers Feit-Thompson conjecture on primes Fermat-Catalan conjecture Fibonacci Primes Firoozbakht's conjecture First Hardy–Littlewood conjecture Formalised Erdős problems (Lean 4) Fortune's Conjecture Four-square conjecture with powers of 2, 3, and 5 Gauss circle problem Gauss circle problem exponent gcd(numerator(H_n), n!) Gilbreath's conjecture GL_2 Ramanujan conjecture exponent Goldbach's conjecture Green's Open Problem 44 Green's Open Problem 64 Grimm's conjecture Half-Fibonacci sequence Hall's conjecture Home primes (OEIS A037274) Hypothesis H Idoneal numbers completeness conjecture Ihara constant over 𝔽_2 Infinite Regular Primes Infinitude of Pell number primes Infinitude of Wall–Sun–Sun primes Integer part of prime(n)/π(n) Integer values of tan(arctan 1 + arctan 2 + ⋯ + arctan n) Juggler conjecture Kummer–Vandiver conjecture Kurepa's conjecture Lander, Parkin, and Selfridge Conjecture Largest odd divisor of a(n-1) + textrmprime(n) Least k > 0 such that (k+1)(k+2)⋯(k+n) + 1 is prime Least k ≥ 1 such that 2 · n^k - 1 is prime Least k such that cyclotomic polynomial Φ_k(n) is prime Least m such that φ(m) = n! Least positive multiple of n in base 10 with digits 0 and 1 Least prime ≥ n Legendre's conjecture Legendre's conjecture Lehmer’s Mahler measure constant Lehmer's Mahler measure problem Lehmer's totient problem Lemoine's conjectures Lindelof (pointwise growth) exponent for the Riemann zeta function Linnik's constant Littlewood conjectures Lychrel numbers in base 10 Magic Squares Mahler's 3/2 Problem Martinet's constant for totally real number fields Mathoverflow 17560 Mathoverflow 75792 Maximum exponent in the prime factorization of n Minimum modulus for the unique multiset-sum problem Multiplicative order of 2 mod 2n+1 No powers as partition numbers Non-Power-of-2 Almost Perfect Numbers Conjecture Normality of Irrational Algebraic Numbers Normality of mathematical constants Number of Abelian cubes of length 3n over an alphabet of size 3 Number of decompositions of 2n+1 into 2p+q, where p and q are both odd primes Number of digits of n raised to the power of the sum of the digits of n Number of odd primes between n^2 and (n+1)^2 with (n/p) = 1 Number of pairs of twin primes between n^2 and (n+1)^2 Number of prime powers q<=n such that also q+2 is a prime power Number of prime powers strictly between n-th prime and (n+1)-th prime Number of primes < n^2 Number of primes < n^3 Number of primes in n-th row of triangle k^2 - k + p_n Number of primes p such that 2^n ≤ p ≤ 2^n + prime(n) Number of primes p such that n^n ≤ p ≤ n^n + n^2 Number of refactorable numbers (A033950) ≤ 10^n Number of squares bmod n Number of symbols '*' and '^' to write the canonical prime factorization of n Number of times n^2 + s^2 is prime for positive integers s < n Number of ways to express n as sum of square, pentagonal, and hexagonal numbers Number of zeros in ternary representation of 2^n Numbers n such that n^2 + π(n) is prime Numbers n such that the perfect deficiency of n is ≤ 10. Numbers n such that φ(n) = φ(n + φ(n)) Numerator of 1/det(M) for M[i,j] = 1/lcm(i,j) Numerator of a sum involving binomial coefficients Numerator of ζ(4n)/ζ(2n)^2 (with a(0)=2 instead of -2) Numerator of Σ_k=1^n 2^k/k. Odious primes minus evil primes among first n primes Open questions about Fermat numbers Open questions on transcendence of numbers Oppermann's Conjecture Partial sums of C(2n, n)^2 Particular values of the Riemann zeta function Pfister's problem on the Pythagoras number of ℝ(X_1, …, X_n) Pierpont primes Pollock's (tetrahedral numbers) conjecture Polya-Vinogradov best constant (squarefree asymptotic) Practical numbers Prime Triplet Conjecture Prime Tuples Conjecture Prime-th recurrence with reversal at each step Primes and perfect squares Primes of the form 2^n + 2^i + 1 Primitive roots of the form k² + 1 Product of two consecutive primes modulo the next prime Quasiperfect Numbers Ramanujan τ-function Rational distance problem Recurrence a(n) = (a(n-1) + a(n-2)) pmod n Recurrence involving LCM: a(n) = x(n+1)/x(n) - 2 Recurrence with bitwise XOR Representations as p + 2^x + 11 · 2^y with p ≡ 1 pmod 6 Representations with prime conditions Riesel Problem Romanoff's constant Rowland-style prime-generating recurrence Rudin's conjecture on squares in arithmetic progressions Schanuel's Conjecture Scholz conjecture on addition chains Schur–Siegel–Smyth trace constant Selberg congruence spectral-gap constant Selfridge's conjectures Serre's uniformity conjecture over the rationals Sierpiński number Singmaster's conjecture Smallest composite c such that textrmprimorial(n) + c is prime Smallest factorial containing exactly n 6's Smallest index k > n such that (p_k+p_k+1)/(p_n+p_n+1) is an integer ≥ 2 Smallest m > 0 such that n · 2^m + 1 is prime Smallest m > 0 such that there are no primes between nm and n(m+1) inclusive. Smallest m such that n^3 + m^3 + 1 is prime Smallest number k such that kn + 1 is prime Smallest number m such that 2^n - m and 2^n + m are primes Smallest palindrome with exactly n divisors Smallest prime ≡ 1 pmod n Smallest prime formed by concatenation n, n-1, …, n-k Smallest r such that (concatenation of n, r times) · 10 + 1 is prime Smallest x such that σ(x) bmod x = n Solitary Numbers Some conjectures about ranks of elliptic curves over ℚ Sum of Fermat number and Mersenne number minus 1: 2^2^n + 2^n - 1 Sum of four squares with square conditions Sum of next n primes Sum of squares of divisors of n Sum of squares of nonacci numbers Sum of three cubes Sum of two numbers with prime conditions Sum of two squares, a power of 3, and a power of 5 Taxicab numbers The (binary) Goldbach conjecture The 1680-Conjecture The Birch and Swinnerton-Dyer conjecture · grand challenge The Catch-Up game and conjecture The Collatz (3n + 1) conjecture The Curling Number Conjecture The Erdős–Moser equation The Erdős–Straus conjecture The Goormaghtigh conjecture The Hasse–Weil conjecture for elliptic curves The irrationality measure of Γ(1/4) The irrationality measure of π The perfect cuboid problem The prime numbers The Riemann Hypothesis · grand challenge The twin prime conjecture and bounded prime gaps The Wirsing Constant Trajectory of 103 under the Reverse and Add! operation in base 3 Triangular matchstick numbers in the class of prime numbers Tug of war score between prime gap increases and decreases Twin prime conjecture Unique Crystal Components Value of n-th cyclotomic polynomial at n Wieferich primes Wilson primes Wolstenholme numbers Wolstenholme Prime Woodall Primes Zagier's Conjecture on Multiple Zeta Values Zaremba’s conjecture constant
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