Integer Explorer Help
Expression Analyzer
| operation | notation | remarks |
|---|
| positive | +a | unary plus |
| negative | -a | unary minus |
| addition | a+b | plus |
| substraction | a-b | minus |
| multiplication | a*b | times |
| remainder | a%b | modulo |
| integer division | a/b | over (integer result) |
| exponention | a^b | power |
| function | notation | remarks |
|---|
| factorial | n! | up to n = 170 |
| permutation or arrangement | P(n, r) | n ⩾ r |
| combination or binomial coefficient (choose) | C(n, r) | n ⩾ r |
| Greatest Common Divisor | GCD(a, b, …) | at least one parameter |
| Least Common Multiple | LCM(a, b, …) | at least one parameter |
| minimum | Min(a, b, …) | at least one parameter |
| maximum | Max(a, b, …) | at least one parameter |
| sum | Sum(a, b, …) | at least one parameter |
| product | Prod(a, b, …) | at least one parameter |
| integer square root | SqRt(a) | integer result |
| integer cubic root | CbRt(a) | integer result |
| random integer | Rand(n) | between 1 and n included |
For functions taking one parameter or more, parentheses are mandatory.
For functions taking exactly one parameter, they are optional.
| sequence | notation | remarks |
|---|
| prime | Prime(n) | up to n = 1000 |
| repunit (Rn is written with n repeated 1s in decimal numeral system) | R(n) | up to n = 309 |
| Mersenne (Mn = 2n-1) | M(n) | up to n = 1024 |
| Fermat (Fermatn = 22n+1) | Fermat(n) | up to n = 9 |
| Fibonacci (F0 = 0, F1 = 1 and Fn = Fn-1 + Fn-2) | F(n) | up to n = 299 |
| triangular numbers (Tn = n(n+1)/2) | T(n) | up to n = 2512 |
For sequences, parentheses are optional.
Examples
| r(r2) | |
| r15/r3/r5 | |
| gcd(r6, 142857) | |
| prime200*prime201 | semi-prime |
| 18!+7 | can take more than 1 second but not much more |
| 170! | huge number but very fast to factorize! |
| f60+f61 | the sum of 2 consecutive Fibonacci numbers is a Fibonacci number |
| P(123456, 4)+1 | P(n, 4)+1 = n×(n+1)×(n+2)×(n+3)+1 is always a square |
| 318665857834031151167461 | Miller-Rabin strong pseudoprime |
| 7323711140672471990827043 | rather large semiprime |