Integer Analyzer

World's Simplest Integer Tool

This online utility analyzes the digit frequency in one or more integers and prints the digit statistics to the screen. You can find the frequency distributions of one, two, three, or more digits, as well as check the Benford's law (first-digit law). You can display the digit count, percentage, and total values, and also choose the format of the output in the options. Created by math nerds from team Browserling.

Tool Options

Digit Options

Enter the lengths of digits that you want to analyze. Use list "1, 2, 4" or range "2-5" formats.
Concatenate multiple input integers together and analyze them as a single integer.
Only look at the leading digit(s) of the input integers. (Useful for verifying the Benford's law.)

Analysis Type

Print the frequency of occurrence of each digit or group of digits.
Print the frequency and percentage of each digit or group of digits.
Print the frequency and total of each digit or group of digits.

Analysis Format

Choose the integer statistics format that you like.

What Is an Integer Analyzer?

With this browser-based program, you can analyze the frequency of digit occurrences in one or more integers. It runs through all the digits in input integers and prints the information about the statistical digit distributions in them. For example, by entering the integer 242555 as input and analyzing single digits, you will get information that this value consists of two twos, one four, and three fives. If you adjust the "Digit Length" option to 2, then you'll get information about two-digit values: "24", "42", and "25" appear 1 time and "55" appears 2 times. Similarly, three-digit values "242", "425", "255", and "555" appear 1 time. To analyze all possible digit lengths, enter the asterisk symbol "*" in the option. You can also specify other digit length values by listing them separated by commas "1, 2, 5" (this will print statistics of single-digits, digit pairs, and five-digit values), using a range "2-4" (this will print statistics of two, three, and four-digit values), or by combining a list and a range "1-3, 5, 6" (this will print statistics of one, two, three, five and six-digit values). By default, the maximum digit length is equal to the longest integer in the input, but if you activate the option "Join All Integers", then the input will be concatenated and all the input values will form a single large integer. You can also quickly generate statistics to check the Benford's law (also know as Newcomb-Benford law or law of anomalous numbers). This law states that most often, the leading digit of statistics taken from real life is 1, while the greater digits 2, 3, … appear as the most significant digit less and less. To verify the first-digit law, enter a set of integer data in the input field and activate the "Anchor at Beginning" option. This option will look only at the first digit of each integer. By default, the program displays only the number of occurrences of digits in the integer, but you can also display the percentages and fractions of the total. You can also choose the analysis output format and display the information as full text, for example, "Digit 5 appears 3 times", via the colon character, for example, "5: 3", or using a dash, for example, "5 – 3". Integerabulous!

Integer Analyzer Examples

Click to try!
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Digit Frequency Distribution

In this example, we analyze the frequency of occurrence of all single-digit values 0 to 9 in multiple integers. To do this, we enter the value "1" into the digit-length option, which corresponds to the analysis of individual digits. We display only the digit counts in the format "digit: number-of-occurrences". As you can see, the most popular digit is 5 and it appears 6 times.

23589 4561 56842 9540 807102 5250
0: 4 1: 2 2: 4 3: 1 4: 3 5: 6 6: 2 7: 1 8: 3 9: 2
Required options
These options will be used automatically if you select this example.
Enter the lengths of digits that you want to analyze. Use list "1, 2, 4" or range "2-5" formats.
Concatenate multiple input integers together and analyze them as a single integer.
Only look at the leading digit(s) of the input integers. (Useful for verifying the Benford's law.)
Print the frequency of occurrence of each digit or group of digits.
Choose the integer statistics format that you like.
click me

Multi-digit Analysis

In this example, we analyze single-digit, two-digit, three-digit, and five-digit sub-integers. To include all of these values in the analysis, we set the analysis length option to "1-3, 5". This way the analysis algorithm looks at all sub-integers of length 1 to 3 and 5. We also activate the "Join All Integers" mode to examine both input integers as one big integer. We use the dash format for the statistics output and display the frequency of the digits together with their total count.

2454 5245
2 – 2 (2/8) 4 – 3 (3/8) 5 – 3 (3/8) 24 – 2 (2/7) 45 – 3 (3/7) 52 – 1 (1/7) 54 – 1 (1/7) 245 – 2 (2/6) 452 – 1 (1/6) 454 – 1 (1/6) 524 – 1 (1/6) 545 – 1 (1/6) 24545 – 1 (1/4) 45245 – 1 (1/4) 45452 – 1 (1/4) 54524 – 1 (1/4)
Required options
These options will be used automatically if you select this example.
Enter the lengths of digits that you want to analyze. Use list "1, 2, 4" or range "2-5" formats.
Concatenate multiple input integers together and analyze them as a single integer.
Only look at the leading digit(s) of the input integers. (Useful for verifying the Benford's law.)
Print the frequency and total of each digit or group of digits.
Choose the integer statistics format that you like.
click me

Verify Benford's Law

In this example, we load country population statistics and verify Newcomb-Benford law. To find how often each leading digit appears in the sample data, we activate the "Anchor at Beginning" option. This option anchors the analysis at the first digit of each integer and discards other digits. This way, we get the frequency distribution of the first digit together with their percentage. We also select the option to print the statistical information in the text format. Looking at the output, we can say that this data follows the Benford law as the smallest leading digits appear often (digit 1 occurs in 40% of cases), while the larger digits are rarely found in the first spot (digit 9 occurs in only 8% of cases).

1404694000 1376404000 329957441 266911900 218481188 211819980 208170076 171049608 146748590 126577691 125950000 112079000 108988550 100791150 96208984 86791000 84342410 83154997 83149300 68859599 66647112 66545883 60238522 55890747 54956900 54045000 51780579 48258494 47564296 46934632 44938712 43053000 42792500 41660982 40006700 39310000 38313035 38206430 36006860 34342017 34218169 32918580 32710000 32225560 32162184 31825000 30418000 30366000 29162000 28609000 25795000 25717000 25680342 25666000 24348251 23782448 22314743 21803000 20870060 19658000 19618065 19401658 19256346 18763165 17861000 17679735 17563749 17522410 17469745 17070000 15948000 15443000 15288489 14645000 12771000 11952693 11722038 11476279 11469896 11333000 11215578 11062000 10911819 10741165 10739000 10693939 10670315 10315244 10313447 10276617 9981500 9771000 9722556 9408400 9158345 9136000 9127000 8902600 8776000 8570146
Digit 1 appears 40 times (40%). Digit 2 appears 15 times (15%). Digit 3 appears 14 times (14%). Digit 4 appears 8 times (8%). Digit 5 appears 4 times (4%). Digit 6 appears 4 times (4%). Digit 8 appears 7 times (7%). Digit 9 appears 8 times (8%).
Required options
These options will be used automatically if you select this example.
Enter the lengths of digits that you want to analyze. Use list "1, 2, 4" or range "2-5" formats.
Concatenate multiple input integers together and analyze them as a single integer.
Only look at the leading digit(s) of the input integers. (Useful for verifying the Benford's law.)
Print the frequency and percentage of each digit or group of digits.
Choose the integer statistics format that you like.

Pro tipsMaster online integer tools

You can pass input to this tool via ?input query argument and it will automatically compute output. Here's how to type it in your browser's address bar. Click to try!

https://onlinetools.com/integer/analyze-integers?input=23589%0A4561%0A56842%0A9540%0A807102%0A5250&digit-length=1&join-integers=false&anchor-at-beginning=false&print-count=true&output-format=colon-format

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These integer tools are on the way!
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Quickly convert integers to base one.

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Quickly convert base one to integers.

Convert Integers to Binary Base

Quickly convert integers to base two.

Convert Binary Base to Integers

Quickly convert base two to integers.

Convert Integers to Octal Base

Quickly convert integers to base eight.

Convert Octal Base to Integers

Quickly convert base eight to integers.

Convert Integers to Hex Base

Quickly convert integers to base sixteen.

Convert Hex Base to Integers

Quickly convert base sixteen to integers.

Convert Integers to Base64

Quickly encode integers to base-64.

Convert Base64 to Integers

Quickly decode base-64 to integers.

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Quickly convert integers to a custom base.

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Quickly encode integers to HTML encoding.

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Quickly decode HTML entities to integers.

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Quickly convert an unsigned integer to a signed integer.

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Quickly calculate the average value of integers.

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Quickly calculate the average value of integer digits.

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Create multiple copies of digits of input integers.

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Quickly find the difference of a bunch of integers.

AND Integers

Quickly apply the bitwise AND operation to integers.

OR Integers

Quickly apply the bitwise OR operation to integers.

XOR Integers

Quickly apply the bitwise XOR operation to integers.

NOT Integers

Quickly apply the bitwise NOT operation to integers.

NAND Integers

Quickly apply the bitwise NAND operation to integers.

NOR Integers

Quickly apply the bitwise NOR operation to integers.

XNOR Integers

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Find integers that match a filter (greater, less, equal).

Right-align Integers

Position all integers so that they align on the right.

Center Integers

Position all integers so that they align in the middle.

Take Absolute Value of Integers

Turn all integers into positive integers.

Make All Integers Negative

Turn all integers into negative integers.

Convert Integers to Fractions

Rewrite an integer in fractional form.

Convert Fractions to Integers

Extract the numerator and denominator from a fraction.

Find and Replace Integers

Search for all occurrences of an integer and replace it.

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Print Increasing Integers

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Print Decreasing Integers

Generate an ordered list of decreasing integers.

Print Integer Information

Quickly find various information about the given integers.

Find Patterns in Integers

Find hidden patterns of numbers in integers.

Calculate Integer Entropy

Find the Shannon entropy of an integer.

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