Random Number Generator

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Random integers are whole numbers chosen from a bounded set, and they are useful for fair draws, simulations, sampling, and quick decisions where bias would mislead results. A random number generator without repeats can cycle through a range so every value appears once before you reset, which is handy for raffles or assigning order fairly.

You define the smallest and largest value, then pick how many numbers to draw each time, and decide whether repeats are allowed. The output shows the latest pick and a running history so you can judge coverage, while summary statistics and a simple frequency view help you spot clustering that occurs by chance.

Try a tight range to inspect behavior, then widen it as your task demands and compare the mean to the midpoint over time. Unique draws reduce duplicates and will eventually exhaust the range, so plan to clear history or expand limits when the app tells you there is nothing new to draw.

Consistency matters for interpretation, so keep the same range when comparing runs and avoid switching options midstream. When results drive a real decision, repeat a few times to see how much they vary and use the distribution, not a single outcome.

Technical Details:

Random integers here come from a finite set observed at a moment in time. Let X be the outcome and define the inclusive bounds min and max. With repeats allowed, each draw is independent and uniformly distributed over the set of integers in the range. With repeats disallowed, sampling proceeds without replacement across the maintained history until all values are used.

The computation maps a uniform real u in the half‑open interval [0, 1) to the integer lattice defined by the bounds. The range size N equals the count of integers between min and max, inclusive. The summary reports the running mean and median of the history so you can compare the central tendency to the range midpoint.

\begin{array}{lll} N & = & \max - \min + 1 \\ X & = & ⌊ u \cdot N ⌋ + \min with u \in [0, 1) \\ P (X = k) & = & \frac{1}{N} for k \in {\min, \dots, \max} \end{array}

Symbols and units used in the computation
Symbol	Meaning	Unit/Datatype	Source
min	Lower inclusive bound	integer	Input
max	Upper inclusive bound	integer	Input
N	Range size (max−min+1)	integer	Derived
n	Quantity per draw	integer ≥ 1	Input
u	Uniform real on [0, 1)	real	Derived
X	Random outcome	integer	Derived
R	Unique values remaining (no‑repeats)	integer	Derived

Worked example

Given min=1 and max=6, the range size is:

N = 6 - 1 + 1 = 6

Suppose u=0.68 on one draw; the mapped outcome is:

X = ⌊ 0.68 \cdot 6 ⌋ + 1 = ⌊ 4.08 ⌋ + 1 = 4 + 1 = 5

With no repeats enabled and three distinct values already seen, the remaining unique count is R=3, so each unseen face then has probability 1⁄3.

Validation & bounds extracted from code

Validation rules and input bounds
Field	Type	Min	Max	Step/Pattern	Error Text	Placeholder
Minimum	integer	−9 007 199 254 740 991	—	—	Enter a valid integer range with Minimum < Maximum and Quantity ≥ 1.	—
Maximum	integer	−9 007 199 254 740 991	—	—	Enter a valid integer range with Minimum < Maximum and Quantity ≥ 1.	—
Quantity per draw	integer	1	—	step = 1	Quantity exceeds the unique values remaining with no‑repeat enabled.	—
No repeat	boolean	—	—	switch	All unique values in the current range are exhausted. Clear history or expand the range.	—

I/O formats & encoding

Inputs and outputs
Input	Accepted Families	Output	Encoding/Precision	Rounding
Bounds and quantity	Integers	Latest value, history, stats	Numbers, CSV (RFC 4180), JSON snapshot	Mean/median displayed with two decimals

Units, precision & rounding policy

All values are integers; the decimal separator for formatted stats is “.” with two digits.
Rounding follows the environment’s standard for fixed‑point formatting at two decimal places.

Randomness, sampling & reproducibility

With repeats: independent uniform draws on integers in the inclusive range.
Without repeats: uniform sampling over unseen integers until the set is exhausted.
No explicit seed is accepted; sequences are not reproducible across sessions.
Histogram shows empirical frequency to help check coverage over time.

Networking & storage behavior

Processing is browser‑based. Exports are created with local blobs for download. Clipboard operations use the platform clipboard API with a safe fallback when permissions are limited.

Performance & complexity

Generation cost is O(n) per draw batch; history lookups and duplicate checks scale with history length.
Histogram preparation is O(H) over history; rendering scales with distinct values in view.

Diagnostics & determinism

Identical inputs produce different sequences by design. Mean and median converge toward the midpoint over many draws with repeats allowed; without repeats, coverage becomes uniform by construction.

Security & privacy

No data is transmitted or stored server‑side. Highlighted JSON is derived from internal data structures. Outcomes are purely random and have no monetary value.

Assumptions & limitations

Heads‑up Large ranges with long histories can slow duplicate checks.
Integers outside the safe 53‑bit range may not be represented exactly.
Range is inclusive of bounds; ensure min < max.
No seeding; sequences cannot be replayed.
No cryptographic guarantees; unsuitable for security‑sensitive use.
Unique mode depends on recorded history; clearing history allows repeats again.
Mean/median formatting is limited to two decimals.
Clipboard access may be denied by the platform.
Downloads can be blocked by popup settings.
JSON payload truncates history to the last 5 000 values.

Edge cases & error sources

Non‑integer inputs are rejected.
Bounds equal or inverted disable generation.
Quantity below 1 is invalid.
Quantity exceeding remaining unique values (no repeats) triggers an error.
Very large integers near ±9 007 199 254 740 991 risk precision issues.
Empty history makes mean and median display as 0.00.
Sorting for median uses ascending numeric order; ties are expected.
Chart may appear empty when no values are generated.
Clipboard fallback can fail in restricted contexts.
Exported CSV must be opened with UTF‑8 support to show symbols correctly.

How‑to · Step‑by‑Step Guide

Random integers for fair draws and simulations, with optional unique coverage.

Enter a Minimum integer.
Enter a Maximum integer greater than the minimum.
Set Quantity per draw for batch generation.
Toggle No repeat to avoid duplicates until reset.
Generate and review the latest value, history, stats, and distribution.

Example: min = 1, max = 100, quantity = 5, no repeats on → five distinct integers between 1 and 100 are added to history.

Pro tip: keep the same range when comparing runs to make mean and coverage comparable.

FAQ

Is my data stored?

No. Generation, history, and exports are handled locally on your device; nothing is sent to a server.

Clipboard and downloads use device‑level APIs.

How accurate is it?

With repeats allowed, each integer has equal chance per draw. Expect variation in small samples; the chart and stats help verify coverage.

What formats can I export?

History exports as CSV with RFC 4180 quoting and as pretty JSON. A structured JSON snapshot also includes inputs, status, stats, and recent history.

Can I use it without connectivity?

Yes. After the page loads, generation and exports work locally. Results do not depend on network access.

Is this suitable for lotteries or gambling?

No. It is not designed for regulated drawings or security‑critical randomness. Use approved systems where required.

How do I generate numbers without repeats?

Enable the no‑repeat option, then generate. Each value appears at most once until you clear history or change the range.

What does a gap in the histogram mean?

It simply means those integers have not been drawn yet. Over more draws, gaps tend to close under uniform sampling.

What license or cost applies?

No purchase or sign‑in prompts appear in the interface. Licensing terms are not displayed within the app.

Troubleshooting

Generate button disabled: ensure integers with min < max and quantity ≥ 1.
Warning about unique values: reduce quantity or clear history, or widen the range.
No downloads: allow downloads for this site or disable popup blocking.
No clipboard copy: grant clipboard permission or use manual copy from JSON/CSV.
Empty chart: generate at least one value; the chart reflects history only.
Slow with huge histories: clear history or temporarily narrow the range.

Blocking error: “Quantity exceeds the unique values remaining with no‑repeat enabled.” Reduce quantity, clear history, or turn repeats on.

Advanced Tips

Tip Use small pilot runs to sanity‑check behavior before long sessions.
Tip Compare mean to the midpoint (min+max)/2 to monitor drift.
Tip In unique mode, watch the remaining count to plan resets.
Tip Keep a fixed range to make runs comparable across days.
Tip Export CSV for quick tallying and JSON for reproducible auditing of inputs and stats.
Tip Use quantity > 1 to create micro‑batches for faster coverage checks.

Glossary

Random integer: A whole number selected by chance from a specified range.
Range: The inclusive set of integers between the minimum and maximum.
Uniform distribution: Each allowed value has the same probability per draw.
Sampling without replacement: Values are not repeated until the set is exhausted.
Quantity per draw: How many integers are generated in one action.
Mean / Median: Average and middle value computed from the history.
Duplicate: A value that appears more than once when repeats are allowed.
Unique remaining: How many unseen integers are left in the current range.