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Tuple in Standard ML, Python, Scala, Swift, Elixir; List in Common Lisp, Python, Scheme, Haskell; Fixed-point number with a variety of precisions and a programmer-selected scale. Complex number in C99, Fortran, Common Lisp, Python, D, Go. This is two floating-point numbers, a real part and an imaginary part.
Python is a high-level, general-purpose programming language. Its design philosophy emphasizes code readability with the use of significant indentation. [33] Python is dynamically type-checked and garbage-collected. It supports multiple programming paradigms, including structured (particularly procedural), object-oriented and functional ...
A snippet of Python code with keywords highlighted in bold yellow font. The syntax of the Python programming language is the set of rules that defines how a Python program will be written and interpreted (by both the runtime system and by human readers). The Python language has many similarities to Perl, C, and Java. However, there are some ...
f p+1 ≡ 0 (mod p), where f k is the k-th Fibonacci number. The first condition is the Fermat primality test using base 2. In general, if p ≡ a (mod x 2 +4), where a is a quadratic non-residue (mod x 2 +4) then p should be prime if the following conditions hold: 2 p−1 ≡ 1 (mod p), f(1) p+1 ≡ 0 (mod p), f(x) k is the k-th Fibonacci ...
For a relational signature X, FO[PFP](X) is the set of formulas formed from X using first-order connectives and predicates, second-order variables as well as a partial fixed point operator used to form formulas of the form [, ], where is a second-order variable, a tuple of first-order variables, a tuple of terms and the lengths of and coincide with the arity of .
A prime divides if and only if p is congruent to ±1 modulo 5, and p divides + if and only if it is congruent to ±2 modulo 5. (For p = 5, F 5 = 5 so 5 divides F 5) . Fibonacci numbers that have a prime index p do not share any common divisors greater than 1 with the preceding Fibonacci numbers, due to the identity: [6]
Prime gaps can be generalized to prime -tuples, patterns in the differences among more than two prime numbers. Their infinitude and density are the subject of the first Hardy–Littlewood conjecture , which can be motivated by the heuristic that the prime numbers behave similarly to a random sequence of numbers with density given by the ...
Because the set of primes is a computably enumerable set, by Matiyasevich's theorem, it can be obtained from a system of Diophantine equations. Jones et al. (1976) found an explicit set of 14 Diophantine equations in 26 variables, such that a given number k + 2 is prime if and only if that system has a solution in nonnegative integers: [7]