1234 (number)

the number 1234 the year 1234 other uses 1234 (disambiguation) 1234 1, 2, 617, 1234 1234 (one thousand two hundred [and] thirty-four) is the natural number following 1233, and preceding 1235.Vanovschi Vitalii Properties of the number 1234 http://www.numberempire.com:80/1234 2026-10-11 www.numberempire.com en Mathematics Prime factorization The prime factorizations of 1234 are 2 and 617, which means that 1234 is the 363rd discrete semiprime, and the 352nd discrete semiprime, since 1234 is the product of exactly two prime numbers.A001358 Semiprimes (or biprimes): products of two primes Decimal properties 1234 is the smallest whole number that contains the digits from 1 through 4 in decimal.Ordered by standard statistical (or Yates) order, the digits "1234" form the fifteenth element in subsets of the natural numbers.A048794 1234 has a prime composite index of 1031,A002808 also the index of the fifth prime repunit (of just 1s) in base-ten, (following , , , and ).A004023 The sum of the base-ten digits of 1234 forms the fourth triangular number, which is 10. 1234 is more specifically the fourth member of the "Triangle of the gods" sequence, obtained by concatenating decimal representations of positive integers.Weisstein Eric W. Eric W. Weisstein Consecutive Number Sequences https://mathworld.wolfram.com/ConsecutiveNumberSequences.html 2026-10-12 MathWorld Wolfram Research, Inc. enA Passion for Mathematics: Numbers, Puzzles, Madness, Religion, and the Quest for Reality Clifford A. Pickover Clifford Pickover Turner Publishing Company 2011 9781118046074 10–11Guy Richard K. Richard Guy Unsolved Problems in Number Theory 3rd Springer 2004 15 978-0-387-20860-2 It is also the fifth member of a related integer sequence, obtained from the recurrence relation starting from and ;A014824 both this sequence and the aforementioned sequence begin in the same way, yet they diverge around their tenth positions. Because it is not divisible by 4, 1234 is the first number in these sequences that is not divisible by its final digit.8 Things to Make and Do in the Fourth Dimension: A Mathematician's Journey Through Narcissistic Numbers, Optimal Dating Algorithms, at Least Two Kinds of Infinity, and More Matt Parker Matt Parker Macmillan 2014 9780374275655 Integer partitions 1234 is the number of integer partitions of 24 without all distinct multiplicities,A336866 Number of integer partitions of n without all distinct multiplicities as well as the number of partitions of 24 into parts that are prime or semiprime.A101049 Number of partitions of n into parts having at most two prime-factors 1234 is the number of "colored" integer partitions of 12 such that four colors are used and parts differ by size, or by color.A327382 Number of colored integer partitions of n such that four colors are used and parts differ by size or by color It is the number of partitions of 332 1089 into exactly four prime numbers.A243940 Number of partitions of n^2 into exactly 4 prime numbers Regarding the fourth non-zero decimal repdigit 44, 1234 is its number of strict partitions containing the sum of some subset of the parts (as a variation of, sum-full strict partitions),A364272 Number of strict integer partitions of n containing the sum of some subset of the parts. A variation of sum-full strict partitions as well as the number of partitions of 44 into parts with an odd number of prime divisors (counted with multiplicity).A286218 Number of partitions of n into parts with an odd number of prime divisors (counted with multiplicity) Binary strings 1234 is the number of "straight" binary strings of length 22 (i.e., the simplest way of representing quantities with binary numbers), equivalently the number of finite Sturmian words of length 22.A005598 a(n) 1 + Sum_{i1..n} (n-i+1)*phi(i) Geometric properties 1234 is the number of integer-sided non-degenerate quadrilaterals with perimeter of 50.A057886 Number of integer 4-tuples that give the lengths of the sides of a nondegenerate quadrilateral with perimeter n T-toothpick sequence 2 300 T-toothpick after 32 steps (A160172).jpg T-toothpick after 33 steps (A160172).jpg T-toothpick after 49 steps (A160172).jpg T-toothpick after 50 steps (A160172).jpg T-Toothpick sequence (with three equal-sized line segments in T shape) after 32, 33 steps (top), and 49, 50 steps (bottom); respectively. Blue toothpicks represent toothpicks added at that step. In a variation of the traditional Toothpick sequence, "T-toothpicks" can be formed with three segments of equal length joined at "pivot points" in the shape of a T, which leaves three "endpoints"; these toothpicks are then attached to each other at pivot points with exposed endpoints only (where allowed, see A160172 for further details).Applegate David David Applegate Pol Omar E. Sloane N. J. A. Neil Sloane The toothpick sequence and other sequences from cellular automata. https://oeis.org/A000695/a000695_1.pdf Congressus Numerantium 206 Combinatorial Press Manitoba 2010 183,184 OEIS 1004.3036 2762248 1262.11046 12655689 A160172 A square fractal-like structure in this sequence is generated at steps (5, 9, 17, 33, ...) while another fractal structure with four squares intersecting a larger square at its corners is generated at steps (6, 12, 25, 49, ...).David Applegate N. J. A. Sloane Neil Sloane Explorations of A139250 (Omar Pol's toothpick sequence) and other toothpick-like sequences. https://oeis.org/A139250/a139250.anim.html The On-Line Encyclopedia of Integer Sequences OEIS Foundation At the thirty-second step, the number of toothpicks is 1234, while at the fiftieth step, the number of toothpicks is 2468, or twice 1234. These represent steps that are one step less than an appearing fractal pattern, and one more (respectively; see image). Vertex sets There are exactly 1234 independent vertex sets in a 4 × 4 square grid.A006506Weisstein Eric W. Hard Square Entropy Constant https://mathworld.wolfram.com/HardSquareEntropyConstant.html 2026-10-12 mathworld.wolfram.com Wolfram Research, Inc. en This is equivalent with the ways of choosing a subset of positions in a 4 × 4 grid so that no two chosen positions are adjacent horizontally or vertically. For the corresponding problem in one dimension instead of two (choosing points from a sequence with no two adjacent), the number of solutions represents a Fibonacci number. Other mathematical properties The expanded form of the number with decimal expansion 1234, would be written as Weisstein Eric W. Expanded Notation https://mathworld.wolfram.com/ExpandedNotation.html 2026-10-12 mathworld.wolfram.com Wolfram Research, Inc. en A parking permutation that avoids 1234 yields a parking function analog of the Schröder numbers.Martinez Lucy Zeilberger Doron 2026 A parking function analog of the Schröder numbers 2609.28650 math.CO In other fields A 2012 study of frequently-used personal identification numbers (PIN) found that, among 4-digit pin codes, 1234 is the most frequently chosen.http://www.datagenetics.com/blog/september32012/ PIN analysis Data Genetics September 3, 2012 Berry N. As cited by Alastair Nisbet Maria Kim 10.4225/75/58a69fd2a8b03 An analysis of chosen alarm code pin numbers & their weakness against a modified brute force attack Johnstone M. 2016 The Proceedings of 14th Australian Information Security Management Conference December 2016 Edith Cowan University Perth, Australia 21–29 https://ro.ecu.edu.au/ism/192 Notes References 1000 Category:Integers