Neil Sloane

Neil James Alexander Sloane is a British-American mathematician. His major contributions are in the fields of combinatorics, error-correcting codes, sphere packing. Sloane is best known for being the creator and maintainer of the On-Line Encyclopedia of Integer Sequences. Sloane was brought up in Australia, he studied at Cornell University under Nick DeClaris, Frank Rosenblatt, Frederick Jelinek and Wolfgang Heinrich Johannes Fuchs, receiving his Ph. D. in 1967. His doctoral dissertation was titled Lengths of Cycle Times in Random Neural Networks. Sloane joined AT&T Bell Labs in 1968 and retired from AT&T Labs in 2012, he became an AT&T Fellow in 1998. He is a Fellow of the Learned Society of Wales, an IEEE Fellow, a Fellow of the American Mathematical Society, a member of the National Academy of Engineering, he is a winner of a Lester R. Ford Award in 1978 and the Chauvenet Prize in 1979. In 2005 Sloane received the IEEE Richard W. Hamming Medal. In 2008 he received the Mathematical Association of America David P. Robbins award, in 2013 the George Pólya Award.

In 2014, to celebrate his 75th birthday, Sloane shared some of his favorite integer sequences. Besides mathematics, he has authored two rock-climbing guides to New Jersey. N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, NY, 1973. F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier/North-Holland, Amsterdam, 1977. M. Harwit and N. J. A. Sloane, Hadamard Transform Optics, Academic Press, San Diego CA, 1979. N. J. A. Sloane and A. D. Wyner, Claude Elwood Shannon: Collected Papers, IEEE Press, NY, 1993. N. J. A. Sloane and S. Plouffe, The Encyclopedia of Integer Sequences, Academic Press, San Diego, 1995. J. H. Conway and N. J. A. Sloane, Sphere Packings and Groups, Springer-Verlag, NY, 1st edn. 1988. A. S. Hedayat, N. J. A. Sloane and J. Stufken, Orthogonal Arrays: Theory and Applications, Springer-Verlag, NY, 1999. G. Nebe, E. M. Rains and N. J. A. Sloane, Self-Dual Codes and Invariant Theory, Springer-Verlag, 2006. Reeds–Sloane algorithm Neil Sloane at the Mathematics Genealogy Project IEEE Richard W. Hamming Medal Recipients, 2005 – Neil J. A. Sloane Neil Sloane's entry in the Numericana Hall of Fame "The pattern collector", Science News Doron Zeilberger, Opinion 124: A Database is Worth a Thousand Mathematical Articles

Isotope

Isotopes are variants of a particular chemical element which differ in neutron number, in nucleon number. All isotopes of a given element have the same number of protons but different numbers of neutrons in each atom; the term isotope is formed from the Greek roots isos and topos, meaning "the same place". It was coined by a Scottish doctor and writer Margaret Todd in 1913 in a suggestion to chemist Frederick Soddy; the number of protons within the atom's nucleus is called atomic number and is equal to the number of electrons in the neutral atom. Each atomic number identifies a specific element, but not the isotope; the number of nucleons in the nucleus is the atom's mass number, each isotope of a given element has a different mass number. For example, carbon-12, carbon-13, carbon-14 are three isotopes of the element carbon with mass numbers 12, 13, 14, respectively; the atomic number of carbon is 6, which means that every carbon atom has 6 protons, so that the neutron numbers of these isotopes are 6, 7, 8 respectively.

A nuclide is a species of an atom with a specific number of protons and neutrons in the nucleus, for example carbon-13 with 6 protons and 7 neutrons. The nuclide concept emphasizes nuclear properties over chemical properties, whereas the isotope concept emphasizes chemical over nuclear; the neutron number has large effects on nuclear properties, but its effect on chemical properties is negligible for most elements. In the case of the lightest elements where the ratio of neutron number to atomic number varies the most between isotopes it has only a small effect, although it does matter in some circumstances; the term isotopes is intended to imply comparison, for example: the nuclides 126C, 136C, 146C are isotopes, but 4018Ar, 4019K, 4020Ca are isobars. However, because isotope is the older term, it is better known than nuclide, is still sometimes used in contexts where nuclide might be more appropriate, such as nuclear technology and nuclear medicine. An isotope and/or nuclide is specified by the name of the particular element followed by a hyphen and the mass number.

When a chemical symbol is used, e.g. "C" for carbon, standard notation is to indicate the mass number with a superscript at the upper left of the chemical symbol and to indicate the atomic number with a subscript at the lower left. Because the atomic number is given by the element symbol, it is common to state only the mass number in the superscript and leave out the atomic number subscript; the letter m is sometimes appended after the mass number to indicate a nuclear isomer, a metastable or energetically-excited nuclear state, for example 180m73Ta. The common pronunciation of the AZE notation is different from how it is written: 42He is pronounced as helium-four instead of four-two-helium, 23592U as uranium two-thirty-five or uranium-two-three-five instead of 235-92-uranium; some isotopes/nuclides are radioactive, are therefore referred to as radioisotopes or radionuclides, whereas others have never been observed to decay radioactively and are referred to as stable isotopes or stable nuclides.

For example, 14C is a radioactive form of carbon, whereas 12C and 13C are stable isotopes. There are about 339 occurring nuclides on Earth, of which 286 are primordial nuclides, meaning that they have existed since the Solar System's formation. Primordial nuclides include 32 nuclides with long half-lives and 253 that are formally considered as "stable nuclides", because they have not been observed to decay. In most cases, for obvious reasons, if an element has stable isotopes, those isotopes predominate in the elemental abundance found on Earth and in the Solar System. However, in the cases of three elements the most abundant isotope found in nature is one long-lived radioisotope of the element, despite these elements having one or more stable isotopes. Theory predicts that many "stable" isotopes/nuclides are radioactive, with long half-lives; some stable nuclides are in theory energetically susceptible to other known forms of decay, such as alpha decay or double beta decay, but no decay products have yet been observed, so these isotopes are said to be "observationally stable".

The predicted half-lives for these nuclides greatly exceed the estimated age of the universe, in fact there are 27 known radionuclides with half-lives longer than the age of the universe. Adding in the radioactive nuclides that have been created artificially, there are 3,339 known nuclides; these include 905 nuclides that are either stable or have half-lives

Hexadecimal

In mathematics and computing, hexadecimal is a positional numeral system with a radix, or base, of 16. It uses sixteen distinct symbols, most the symbols "0"–"9" to represent values zero to nine, "A"–"F" to represent values ten to fifteen. Hexadecimal numerals are used by computer system designers and programmers, as they provide a more human-friendly representation of binary-coded values; each hexadecimal digit represents four binary digits known as a nibble, half a byte. For example, a single byte can have values ranging from 0000 0000 to 1111 1111 in binary form, which can be more conveniently represented as 00 to FF in hexadecimal. In mathematics, a subscript is used to specify the radix. For example the decimal value 10,995 would be expressed in hexadecimal as 2AF316. In programming, a number of notations are used to support hexadecimal representation involving a prefix or suffix; the prefix 0x is used in C and related languages, which would denote this value by 0x2AF3. Hexadecimal is used in the transfer encoding Base16, in which each byte of the plaintext is broken into two 4-bit values and represented by two hexadecimal digits.

In contexts where the base is not clear, hexadecimal numbers can be ambiguous and confused with numbers expressed in other bases. There are several conventions for expressing values unambiguously. A numerical subscript can give the base explicitly: 15910 is decimal 159; some authors prefer a text subscript, such as 159decimal and 159hex, or 159h. In linear text systems, such as those used in most computer programming environments, a variety of methods have arisen: In URIs, character codes are written as hexadecimal pairs prefixed with %: http://www.example.com/name%20with%20spaces where %20 is the space character, ASCII code point 20 in hex, 32 in decimal. In XML and XHTML, characters can be expressed as hexadecimal numeric character references using the notation ode, thus ’. In the Unicode standard, a character value is represented with U+ followed by the hex value, e.g. U+20AC is the Euro sign. Color references in HTML, CSS and X Window can be expressed with six hexadecimal digits prefixed with #: white, for example, is represented #FFFFFF.

CSS allows 3-hexdigit abbreviations with one hexdigit per component: #FA3 abbreviates #FFAA33. Unix shells, AT&T assembly language and the C programming language use the prefix 0x for numeric constants represented in hex: 0x5A3. Character and string constants may express character codes in hexadecimal with the prefix \x followed by two hex digits:'\x1B' represents the Esc control character. To output an integer as hexadecimal with the printf function family, the format conversion code %X or %x is used. In MIME quoted-printable encoding, characters that cannot be represented as literal ASCII characters are represented by their codes as two hexadecimal digits prefixed by an equal to sign =, as in Espa=F1a to send "España". In Intel-derived assembly languages and Modula-2, hexadecimal is denoted with a suffixed H or h: FFh or 05A3H; some implementations require a leading zero when the first hexadecimal digit character is not a decimal digit, so one would write 0FFh instead of FFh Other assembly languages, Delphi, some versions of BASIC, GameMaker Language and Forth use $ as a prefix: $5A3.

Some assembly languages use the notation H'ABCD'. Fortran 95 uses Z'ABCD'. Ada and VHDL enclose hexadecimal numerals in based "numeric quotes": 16#5A3#. For bit vector constants VHDL uses the notation x"5A3". Verilog represents hexadecimal constants in the form 8'hFF, where 8 is the number of bits in the value and FF is the hexadecimal constant; the Smalltalk language uses the prefix 16r: 16r5A3 PostScript and the Bourne shell and its derivatives denote hex with prefix 16#: 16#5A3. For PostScript, binary data can be expressed as unprefixed consecutive hexadecimal pairs: AA213FD51B3801043FBC... Common Lisp uses the prefixes # 16r. Setting the variables *read-base* and *print-base* to 16 can be used to switch the reader and printer of a Common Lisp system to Hexadecimal number representation for reading and printing numbers, thus Hexadecimal numbers can be represented without the #x or #16r prefix code, when the input or output base has been changed to 16. MSX BASIC, QuickBASIC, FreeBASIC and Visual Basic prefix hexadecimal numbers with &H: &H5A3 BBC BASIC and Locomotive BASIC use & for hex.

TI-89 and 92 series uses a 0h prefix: 0h5A3 ALGOL 68 uses the prefix 16r to denote hexadecimal numbers: 16r5a3. Binary and octal numbers can be specified similarly; the most common format for hexadecimal on IBM mainframes and midrange computers running the traditional OS's is X'5A3', is used in Assembler, PL/I, COBOL, JCL, scripts and other places. This format was common on

Roman numerals

The numeric system represented by Roman numerals originated in ancient Rome and remained the usual way of writing numbers throughout Europe well into the Late Middle Ages. Numbers in this system are represented by combinations of letters from the Latin alphabet. Roman numerals, as used today, employ seven symbols, each with a fixed integer value, as follows: The use of Roman numerals continued long after the decline of the Roman Empire. From the 14th century on, Roman numerals began to be replaced in most contexts by the more convenient Arabic numerals; the original pattern for Roman numerals used the symbols I, V, X as simple tally marks. Each marker for 1 added a unit value up to 5, was added to to make the numbers from 6 to 9: I, II, III, IIII, V, VI, VII, VIII, VIIII, X; the numerals for 4 and 9 proved problematic, are replaced with IV and IX. This feature of Roman numerals is called subtractive notation; the numbers from 1 to 10 are expressed in Roman numerals as follows: I, II, III, IV, V, VI, VII, VIII, IX, X.

The system being decimal and hundreds follow the same underlying pattern. This is the key to understanding Roman numerals: Thus 10 to 100: X, XX, XXX, XL, L, LX, LXX, LXXX, XC, C. Note that 40 and 90 follow the same subtractive pattern as 4 and 9, avoiding the confusing XXXX. 100 to 1000: C, CC, CCC, CD, D, DC, DCC, DCCC, CM, M. Again - 400 and 900 follow the standard subtractive pattern, avoiding CCCC. In the absence of standard symbols for 5,000 and 10,000 the pattern breaks down at this point - in modern usage M is repeated up to three times; the Romans had several ways to indicate larger numbers, but for practical purposes Roman Numerals for numbers larger than 3,999 are if used nowadays, this suffices. M, MM, MMM. Many numbers include hundreds and tens; the Roman numeral system being decimal, each power of ten is added in descending sequence from left to right, as with Arabic numerals. For example: 39 = "Thirty nine" = XXXIX. 246 = "Two hundred and forty six" = CCXLVI. 421 = "Four hundred and twenty one" = CDXXI.

As each power of ten has its own notation there is no need for place keeping zeros, so "missing places" are ignored, as in Latin speech, thus: 160 = "One hundred and sixty" = CLX 207 = "Two hundred and seven" = CCVII 1066 = "A thousand and sixty six" = MLXVI. Roman numerals for large numbers are nowadays seen in the form of year numbers, as in these examples: 1776 = MDCCLXXVI. 1954 = MCMLIV 1990 = MCMXC. 2014 = MMXIV (the year of the games of the XXII Olympic Winter Games The current year is MMXIX. The "standard" forms described above reflect typical modern usage rather than an unchanging and universally accepted convention. Usage in ancient Rome varied and remained inconsistent in medieval times. There is still no official "binding" standard, which makes the elaborate "rules" used in some sources to distinguish between "correct" and "incorrect" forms problematic. "Classical" inscriptions not infrequently use IIII for "4" instead of IV. Other "non-subtractive" forms, such as VIIII for IX, are sometimes seen, although they are less common.

On the numbered gates to the colosseum, for instance, IV is systematically avoided in favour of IIII, but other "subtractives" apply, so that gate 44 is labelled XLIIII. Isaac Asimov speculates that the use of "IV", as the initial letters of "IVPITER" may have been felt to have been impious in this context. Clock faces that use Roman numerals show IIII for four o'clock but IX for nine o'clock, a practice that goes back to early clocks such as the Wells Cathedral clock of the late 14th century. However, this is far from universal: for example, the clock on the Palace of Westminster, Big Ben, uses a "normal" IV. XIIX or IIXX are sometimes used for "18" instead of XVIII; the Latin word for "eighteen" is rendered as the equivalent of "two less than twenty" which may be the source of this usage. The standard forms for 98 and 99 are XCVIII and XCIX, as described in the "decimal pattern" section above, but these numbers are rendered as IIC and IC originally from the Latin duodecentum and undecentum.

Sometimes V and L are not used, with instances such as IIIIII and XXXXXX rather than VI or LX. Most non-standard numerals other than those described above - such as VXL for 45, instead of the standard XLV are modern and may be due to error rather than being genuine variant usage. In the early years of the 20th century, different representations of 900 appeared in several inscribed dates. For instance, 1910 is shown on Admiralty Arch, London, as MDCCCCX rather than MCMX, while on the north entrance to the Saint Louis Art Museum, 1903 is inscribed as MDCDIII rather than MCMIII. Although Roman numerals came to be written with letters

Factorization

In mathematics, factorization or factoring consists of writing a number or another mathematical object as a product of several factors smaller or simpler objects of the same kind. For example, 3 × 5 is a factorization of the integer 15, is a factorization of the polynomial x2 – 4. Factorization is not considered meaningful within number systems possessing division, such as the real or complex numbers, since any x can be trivially written as × whenever y is not zero. However, a meaningful factorization for a rational number or a rational function can be obtained by writing it in lowest terms and separately factoring its numerator and denominator. Factorization was first considered by ancient Greek mathematicians in the case of integers, they proved the fundamental theorem of arithmetic, which asserts that every positive integer may be factored into a product of prime numbers, which cannot be further factored into integers greater than 1. Moreover, this factorization is unique up to the order of the factors.

Although integer factorization is a sort of inverse to multiplication, it is much more difficult algorithmically, a fact, exploited in the RSA cryptosystem to implement public-key cryptography. Polynomial factorization has been studied for centuries. In elementary algebra, factoring a polynomial reduces the problem of finding its roots to finding the roots of the factors. Polynomials with coefficients in the integers or in a field possess the unique factorization property, a version of the fundamental theorem of arithmetic with prime numbers replaced by irreducible polynomials. In particular, a univariate polynomial with complex coefficients admits a unique factorization into linear polynomials: this is a version of the fundamental theorem of algebra. In this case, the factorization can be done with root-finding algorithms; the case of polynomials with integer coefficients is fundamental for computer algebra. There are efficient computer algorithms for computing factorizations within the ring of polynomials with rational number coefficients.

A commutative ring possessing the unique factorization property is called a unique factorization domain. There are number systems, such as certain rings of algebraic integers, which are not unique factorization domains. However, rings of algebraic integers satisfy the weaker property of Dedekind domains: ideals factor uniquely into prime ideals. Factorization may refer to more general decompositions of a mathematical object into the product of smaller or simpler objects. For example, every function may be factored into the composition of a surjective function with an injective function. Matrices possess many kinds of matrix factorizations. For example, every matrix has a unique LUP factorization as a product of a lower triangular matrix L with all diagonal entries equal to one, an upper triangular matrix U, a permutation matrix P. By the fundamental theorem of arithmetic, every integer greater than 1 has a unique factorization into prime numbers, which are those integers which cannot be further factorized into the product of integers greater than one.

For computing the factorization of an integer n, one needs an algorithm for finding a divisor q of n or deciding that n is prime. When such a divisor is found, the repeated application of this algorithm to the factors q and n / q gives the complete factorization of n. For finding a divisor q of n, if any, it suffices to test all values of q such that 1 < q and q2 ≤ n. In fact, if r is a divisor of n such that r2 > n q = n / r is a divisor of n such that q2 ≤ n. If one tests the values of q in increasing order, the first divisor, found is a prime number, the cofactor r = n / q cannot have any divisor smaller than q. For getting the complete factorization, it suffices thus to continue the algorithm by searching a divisor of r, not smaller than q and not greater than √r. There is no need to test all values of q for applying the method. In principle, it suffices to test only prime divisors; this needs to have a table of prime numbers that may be generated for example with the sieve of Eratosthenes.

As the method of factorization does the same work as the sieve of Eratosthenes, it is more efficient to test for a divisor only those numbers for which it is not clear whether they are prime or not. One may proceed by testing 2, 3, 5, the numbers > 5, whose last digit is 1, 3, 7, 9 and the sum of digits is not a multiple of 3. This method is inefficient for larger integers. For example, Pierre de Fermat was unable to discover that the 6th Fermat number 1 + 2 2 5 = 1 + 2 32 = 4 294 967 297 is not a prime number. In fact, applying the above method would require more than 10000 divisions, for a number that has 10 decimal digits. There are more efficient factoring algorithms; however they remain inefficient, as, with the present state of the art, one cannot factorize with the more powerful computers, a number of 500 decimal digits, the product of two randomly chosen prime numbers. This insures the security of the RSA cryptosystem, used for secure internet communication. For fa

100 (number)

100 or one hundred is the natural number following 99 and preceding 101. In medieval contexts, it may be described as the short hundred or five score in order to differentiate the English and Germanic use of "hundred" to describe the long hundred of six score or 120. 100 is the square of 10. The standard SI prefix for a hundred is "hecto-". 100 is the basis of percentages. 100 is the sum of the first nine prime numbers, as well as the sum of some pairs of prime numbers e.g. 3 + 97, 11 + 89, 17 + 83, 29 + 71, 41 + 59, 47 + 53. 100 is the sum of the cubes of the first four integers. This is related by Nicomachus's theorem to the fact that 100 equals the square of the sum of the first four integers: 100 = 102 = 2.26 + 62 = 100, thus 100 is a Leyland number.100 is an 18-gonal number. It is divisible by 25, the number of primes below it, it can not be expressed as the difference between any integer and the total of coprimes below it, making it a noncototient. It can be expressed as a sum of some of its divisors.

100 is a Harshad number in base 10, in base 4, in that base it is a self-descriptive number. There are 100 prime numbers whose digits are in ascending order. 100 is the smallest number. One hundred is the atomic number of fermium, an actinide and the first of the heavy metals that cannot be created through neutron bombardment. On the Celsius scale, 100 degrees is the boiling temperature of pure water at sea level; the Kármán line lies at an altitude of 100 kilometres above the Earth's sea level and is used to define the boundary between Earth's atmosphere and outer space. There are 100 blasts of the Shofar heard in the service of the Jewish New Year. A religious Jew is expected to utter at least 100 blessings daily. In the Hindu book of the Mahabharata, the king Dhritarashtra had 100 sons known as the Kauravas; the United States Senate has 100 Senators. Most of the world's currencies are divided into 100 subunits; the 100 Euro banknotes feature a picture of a Rococo gateway on the obverse and a Baroque bridge on the reverse.

The U. S. hundred-dollar bill has Benjamin Franklin's portrait. S. bill in print. American savings bonds of $100 have Thomas Jefferson's portrait, while American $100 treasury bonds have Andrew Jackson's portrait. One hundred is also: The number of years in a century; the number of pounds in an American short hundredweight. In Greece, India and Nepal, 100 is the police telephone number. In Belgium, 100 is the firefighter telephone number. In United Kingdom, 100 is the operator telephone number; the HTTP status code indicating that the client should continue with its request. The 100 The age at which a person becomes a centenarian; the number of yards in an American football field. The number of runs required for a cricket batsman to score a significant milestone; the number of points required for a snooker player to score a century break, a significant milestone. The record number of points scored in one NBA game by a single player, set by Wilt Chamberlain of the Philadelphia Warriors on March 2, 1962.

1 vs. 100 AFI's 100 Years... Hundred Hundred Hundred Days Hundred Years' War List of highways numbered 100 Top 100 Greatest 100 Wells, D; the Penguin Dictionary of Curious and Interesting Numbers London: Penguin Group.: 133 Chisholm, Hugh, ed.. "Hundred". Encyclopædia Britannica. Cambridge University Press. On the Number 100

Californium

Californium is a radioactive chemical element with symbol Cf and atomic number 98. The element was first synthesized in 1950 at the Lawrence Berkeley National Laboratory, by bombarding curium with alpha particles, it is an actinide element, the sixth transuranium element to be synthesized, has the second-highest atomic mass of all the elements that have been produced in amounts large enough to see with the unaided eye. The element was named after the state of California. Two crystalline forms exist for californium under normal pressure: one above and one below 900 °C. A third form exists at high pressure. Californium tarnishes in air at room temperature. Compounds of californium are dominated by the +3 oxidation state; the most stable of californium's twenty known isotopes is californium-251, which has a half-life of 898 years. This short half-life means. Californium-252, with a half-life of about 2.645 years, is the most common isotope used and is produced at the Oak Ridge National Laboratory in the United States and the Research Institute of Atomic Reactors in Russia.

Californium is one of the few transuranium elements. Most of these applications exploit the property of certain isotopes of californium to emit neutrons. For example, californium can be used to help start up nuclear reactors, it is employed as a source of neutrons when studying materials using neutron diffraction and neutron spectroscopy. Californium can be used in nuclear synthesis of higher mass elements. Users of californium must take into account radiological concerns and the element's ability to disrupt the formation of red blood cells by bioaccumulating in skeletal tissue. Californium is a silvery white actinide metal with a melting point of 900 ± 30 °C and an estimated boiling point of 1,745 K; the pure metal is malleable and is cut with a razor blade. Californium metal starts to vaporize above 300 °C. Below 51 K californium metal is either ferromagnetic or ferrimagnetic, between 48 and 66 K it is antiferromagnetic, above 160 K it is paramagnetic, it forms alloys with lanthanide metals but little is known about them.

The element has two crystalline forms under 1 standard atmosphere of pressure: a double-hexagonal close-packed form dubbed alpha and a face-centered cubic form designated beta. The α form exists below 600–800 °C with a density of 15.10 g/cm3 and the β form exists above 600–800 °C with a density of 8.74 g/cm3. At 48 GPa of pressure the β form changes into an orthorhombic crystal system due to delocalization of the atom's 5f electrons, which frees them to bond; the bulk modulus of a material is a measure of its resistance to uniform pressure. Californium's bulk modulus is 50±5 GPa, similar to trivalent lanthanide metals but smaller than more familiar metals, such as aluminium. Californium exhibits oxidation states of 4, 3, or 2, it forms eight or nine bonds to surrounding atoms or ions. Its chemical properties are predicted to be similar to other 3+ valence actinide elements and the element dysprosium, the lanthanide above californium in the periodic table; the element tarnishes in air at room temperature, with the rate increasing when moisture is added.

Californium reacts when heated with nitrogen, or a chalcogen. Californium is only water-soluble as the californium cation. Attempts to reduce or oxidize the +3 ion in solution have failed; the element forms a water-soluble chloride, nitrate and sulfate and is precipitated as a fluoride, oxalate, or hydroxide. Californium is the heaviest actinide to exhibit covalent properties, as is observed in the californium borate. Twenty radioisotopes of californium have been characterized, the most stable being californium-251 with a half-life of 898 years, californium-249 with a half-life of 351 years, californium-250 with a half-life of 13.08 years, californium-252 with a half-life of 2.645 years. All the remaining isotopes have half-lives shorter than a year, the majority of these have half-lives shorter than 20 minutes; the isotopes of californium range in mass number from 237 to 256. Californium-249 is formed from the beta decay of berkelium-249, most other californium isotopes are made by subjecting berkelium to intense neutron radiation in a nuclear reactor.

Although californium-251 has the longest half-life, its production yield is only 10% due to its tendency to collect neutrons and its tendency to interact with other particles. Californium-252 is a strong neutron emitter, which makes it radioactive and harmful. Californium-252 undergoes alpha decay 96.9% of the time to form curium-248 while the remaining 3.1% of decays are spontaneous fission. One microgram of californium-252 emits 2.3 million neutrons per second, an average of 3.7 neutrons per spontaneous fission. Most of the other isotopes of californium decay to isotopes of curium via alpha decay. Californium was first synthesized at the University of California Radiation Laboratory in Berkeley, by the physics researchers Stanley G. Thompson, Kenneth Street, Jr. Albert Ghiorso, Glenn T. Seaborg on or about February 9, 1950, it was the sixth transuranium element to be dis