Special Number Generator
Generate square / cube / triangular / prime / Fibonacci / perfect numbers in one click. Every value uses big-integer maths, so long results stay exact.
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| No. | Result | Expression |
|---|
Introduction to the tool and how to use it
The special-number generator lists the commonly used families of regular numbers in one place, handy for math problems, practice sheets, sequence checks, or simply seeing what large numbers look like. Supported types:
1. Squares: n × n, such as 1, 4, 9, 16 …;
2. Cubes: n × n × n, such as 1, 8, 27, 64 …;
3. Triangular numbers: n × (n+1) ÷ 2, such as 1, 3, 6, 10 …;
4. Primes: the n-th prime in order, such as 2, 3, 5, 7, 11 …;
5. Fibonacci: F(1)=1, F(2)=1, and each later term equals the sum of the previous two, such as 1, 1, 2, 3, 5, 8 …;
6. Perfect numbers: numbers equal to the sum of their proper divisors, such as 6, 28, 496, 8128 …; this tool computes them directly with the Euclid formula 2^(p-1) × (2^p - 1) and returns results instantly.
Note: all values use big-integer arithmetic, so even very long digits suffer no floating-point error or scientific notation. Primes go up to the 100000th, Fibonacci to the 5000th term, and perfect numbers are limited to 12 by known Mersenne primes; when the starting index is out of range, generation wraps to the beginning and a notice is shown.
1. Squares: n × n, such as 1, 4, 9, 16 …;
2. Cubes: n × n × n, such as 1, 8, 27, 64 …;
3. Triangular numbers: n × (n+1) ÷ 2, such as 1, 3, 6, 10 …;
4. Primes: the n-th prime in order, such as 2, 3, 5, 7, 11 …;
5. Fibonacci: F(1)=1, F(2)=1, and each later term equals the sum of the previous two, such as 1, 1, 2, 3, 5, 8 …;
6. Perfect numbers: numbers equal to the sum of their proper divisors, such as 6, 28, 496, 8128 …; this tool computes them directly with the Euclid formula 2^(p-1) × (2^p - 1) and returns results instantly.
Note: all values use big-integer arithmetic, so even very long digits suffer no floating-point error or scientific notation. Primes go up to the 100000th, Fibonacci to the 5000th term, and perfect numbers are limited to 12 by known Mersenne primes; when the starting index is out of range, generation wraps to the beginning and a notice is shown.
How to use
- Choose a type.
- Set the starting index, that is, which term to begin from; for triangular numbers, entering 5 starts at T(5)=15.
- Set how many values to generate.
- Choose the sort order as needed: keep original order (ascending by index), ascending, or descending.
- Set the separator; the default \\n puts one number per line, and switching to a half-width comma joins them onto one line.
- Click Start; results appear in both the text box and the table below (index / value / expression), and the table can be downloaded as CSV.
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