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.
Type:
Start Index:
How Many:
Sort by:
Separator:
Output Result
Generated Number
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| No. | Result | Expression |
|---|
Introduction to the tool and how to use it
Special Number Generator lists the classic families of patterned numbers in one go — handy for maths practice, worksheets, checking a sequence, or just seeing what a huge number looks like. Supported types:
1. Square numbers: n × n → 1, 4, 9, 16 …;
2. Cube numbers: n × n × n → 1, 8, 27, 64 …;
3. Triangular numbers: n × (n+1) ÷ 2 → 1, 3, 6, 10 …;
4. Primes: the n-th prime in order → 2, 3, 5, 7, 11 …;
5. Fibonacci numbers: F(1)=1, F(2)=1, each later term is the sum of the previous two → 1, 1, 2, 3, 5, 8 …;
6. Perfect numbers: equal to the sum of their proper divisors → 6, 28, 496, 8128 … computed instantly with the Euclid formula 2^(p-1) × (2^p - 1).
Steps:
1. Pick a Type;
2. Set Start Index — which term to begin at, e.g. 5 for triangular numbers starts at T(5)=15;
3. Set Generate Count;
4. Optionally choose a Sort By: keep original order (by index), ascending or descending;
5. Set the separator — the default \n puts one number per line, a comma joins them on one line;
6. Click Run. Results appear in the text box and in the table below (index / value / formula), with CSV export.
Note: every value is computed with big integers, so long terms never suffer floating-point error or scientific notation. Primes go up to the 100000th, Fibonacci up to term 5000, and perfect numbers are limited to the 12 known Mersenne exponents; a start index beyond the range restarts from the beginning and shows a hint.
1. Square numbers: n × n → 1, 4, 9, 16 …;
2. Cube numbers: n × n × n → 1, 8, 27, 64 …;
3. Triangular numbers: n × (n+1) ÷ 2 → 1, 3, 6, 10 …;
4. Primes: the n-th prime in order → 2, 3, 5, 7, 11 …;
5. Fibonacci numbers: F(1)=1, F(2)=1, each later term is the sum of the previous two → 1, 1, 2, 3, 5, 8 …;
6. Perfect numbers: equal to the sum of their proper divisors → 6, 28, 496, 8128 … computed instantly with the Euclid formula 2^(p-1) × (2^p - 1).
Steps:
1. Pick a Type;
2. Set Start Index — which term to begin at, e.g. 5 for triangular numbers starts at T(5)=15;
3. Set Generate Count;
4. Optionally choose a Sort By: keep original order (by index), ascending or descending;
5. Set the separator — the default \n puts one number per line, a comma joins them on one line;
6. Click Run. Results appear in the text box and in the table below (index / value / formula), with CSV export.
Note: every value is computed with big integers, so long terms never suffer floating-point error or scientific notation. Primes go up to the 100000th, Fibonacci up to term 5000, and perfect numbers are limited to the 12 known Mersenne exponents; a start index beyond the range restarts from the beginning and shows a hint.
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