Contents
How the superfactorial calculator works
Enter a whole number n. The calculator builds 1!, 2!, and every factorial through n!, multiplies them together, and returns the exact integer sf(n).
One product contains many factorials
The definition used here is 1! × 2! × … × n!. For n = 4, the factors are 1, 2, 6, and 24, so sf(4) = 288. Open the expansion below the result to verify the symbolic chain and its last factorial.
A useful recurrence is . Dividing consecutive values should therefore return n!.
Checks from small to large
sf(3) = 12. Multiply 1! × 2! × 3! = 1 × 2 × 6.
sf(5) = 34,560. The previous value 288 receives the new factor 5! = 120.
sf(6) = 24,883,200. The ratio sf(6) / sf(5) equals 720, exactly 6!.
sf(10) has 28 digits. Its exact value is 6,658,606,584,104,736,522,240,000,000, already too large for ordinary fixed-precision integer storage.
Boundary values and similar names
sf(0) equals 1 because no factorials are selected and the empty product is defined as 1. This also makes sf(1) = sf(0) × 1! work without a special exception.
A superfactorial is not n!! and not (n!)!. Double factorial skips every other integer; a factorial of a factorial applies ! twice in sequence. Those operations produce different values.
The calculator accepts integers from 0 through 110. At the upper limit the answer has 8,632 digits. Display spaces only group a long number for reading; copying returns every digit without separators or rounding.
Questions about superfactorials
The name has been used for more than one fast-growing function, so the displayed product is the safest way to identify this definition.
What is sf(n)?
Here sf(n) is the product 1! × 2! × … × n!, including each ordinary factorial up to n!.
Why is sf(0) equal to 1?
There are no factors at n = 0. The empty product is defined as 1, preserving the recurrence from the first step.
Is a superfactorial the same as a double factorial?
No. n!! multiplies integers in steps of two, whereas sf(n) multiplies consecutive factorials.
How can I check a large result?
Divide sf(n) by sf(n − 1). The quotient must equal n!.
Are long answers rounded?
No. The calculator uses exact arbitrary-length integers and retains every digit within the input limit.
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