Mathematics · Algebra
Prime Number Checker
Determine whether a positive whole number is prime.
Inputs and results stay in this browser. Change one value at a time to explore the relationship.
Calculation steps
- Test possible divisors through √97=9.848857801796104.
- 97 is prime.
Understand Prime checker
One idea, three depths
Choose how deeply to explain Prime checker
Prime checker: Determine whether a positive whole number is prime.
Age 5Explain it to a 5-year-oldStart with a picture
Imagine using Prime checker to answer this question: determine whether a positive whole number is prime? Enter Whole number n; the calculator shows Prime (1=yes, 0=no). For example: 97 is prime because no integer from 2 through 9 divides it. The answer tells you Prime (1=yes, 0=no).
Age 15Explain it to a 15-year-oldConnect it to the formula
A composite number must have at least one factor no larger than its square root. The rule is Test divisors d≤√n. Its input values are Whole number n, and the main result is Prime (1=yes, 0=no). For example: 97 is prime because no integer from 2 through 9 divides it.
CollegeExplain it at college levelState the model precisely
This calculator evaluates the stated prime checker relation over the valid integer domain stated below. The implemented relation is Test divisors d≤√n, evaluated from Whole number n to produce Prime (1=yes, 0=no). A composite number must have at least one factor no larger than its square root. One is neither prime nor composite.
Inputs and valid domain
- Whole number n must be an integer, at least 1, at most 1000000000000.
Important boundary: One is neither prime nor composite.
The formula
Test divisors d≤√n
How the calculator works through it
It substitutes Whole number n into the formula and exposes every numerical step above. The main output is Prime (1=yes, 0=no), accompanied by Smallest divisor found, Square-root limit.
Read the result correctly
The Prime (1=yes, 0=no) is the direct answer to “determine whether a positive whole number is prime.” Read it with the units shown beside the inputs; a sign, angle, percentage or rate changes what the number means.
A worked check
97 is prime because no integer from 2 through 9 divides it.
Where this model stops being reliable
One is neither prime nor composite.
Learn it by changing one value
Begin with the worked example, then change one value while keeping the others fixed. Compare the new result and calculation steps to identify which part of the formula changed.
Dictionary terms behind this calculator
Before studying the codeWhat you should know firstUse the calculator immediately, or check the foundations before reading the implementation.
These foundations help you understand why Prime checker works. They never block the calculator, and “optional” means useful context rather than a hidden requirement.
Hard requirements
- Reading formulas and substituting values
Prime checker uses Test divisors d≤√n. You need to recognise what each side represents before substituting the stated inputs or rearranging the relationship.
Review this foundation about 4 min
Strong support
- Functions and input-output rules
A function viewpoint helps you see how changing an input changes the Prime checker result.
Review this foundation about 5 min
Optional enrichment
- Powers and exponents
Powers are not required for every Prime checker calculation, but they make related algebraic forms and code easier to read.
Review this foundation about 4 min
Mathematics → algorithm → program
Implement this calculation in code
These are direct reference implementations of the calculator's principal relationship and first output. They run locally and include a small known-answer check where the language supports it.
Algorithm
- Reject values below two and handle two separately.
- Reject even values.
- Test odd divisors while d*d is no greater than n.
Python
def is_prime(n: int) -> int:
if n < 2: return 0
if n == 2: return 1
if n % 2 == 0: return 0
d = 3
while d * d <= n:
if n % d == 0: return 0
d += 2
return 1
assert is_prime(97) == 1
C
#include <assert.h>
#include <stdint.h>
int is_prime(uint64_t n){if(n<2)return 0;if(n==2)return 1;if(!(n&1))return 0;for(uint64_t d=3;d<=n/d;d+=2)if(n%d==0)return 0;return 1;}
int main(void){assert(is_prime(97)==1);}
C++
#include <cassert>
#include <cstdint>
int is_prime(std::uint64_t n){if(n<2)return 0;if(n==2)return 1;if(!(n&1))return 0;for(std::uint64_t d=3;d<=n/d;d+=2)if(n%d==0)return 0;return 1;}
int main(){assert(is_prime(97)==1);}
Linux x86-64 assembly
x86-64 NASM · System V ABI · Linux · integer arguments in rdi, rsi and rdx
; uint64_t is_prime(uint64_t n), returns 1 or 0
global is_prime
section .text
is_prime:
cmp rdi, 2
jb .no
je .yes
test dil, 1
jz .no
mov rcx, 3
.loop:
mov rax, rcx
imul rax, rcx
cmp rax, rdi
ja .yes
mov rax, rdi
xor edx, edx
div rcx
test rdx, rdx
jz .no
add rcx, 2
jmp .loop
.yes:
mov eax, 1
ret
.no:
xor eax, eax
ret
MATLAB
function result = is_prime(n)
result = double(isprime(round(n)));
end
Wolfram Language
ClearAll[mwCalculate];
mwCalculate[n_Integer] := Boole[PrimeQ[n]];
Continue in mathematical software
The downloaded file includes your current inputs and first calculated result. It is created locally.
Floating-point answers can differ slightly by language, compiler and processor. Compare within a suitable tolerance rather than assuming every decimal representation will be identical.
Supporting sourcesAcademic referencesPrimary standards, textbooks and complete citations
Standards, reading and academic references
Use the calculator as the worked interaction, then consult the primary standards and academic textbooks listed below. MW SysArc links to the original sources; the explanation on this page is original and does not reproduce them.
Algebra and Trigonometry 2e
Read the related free OpenStax mathematics chaptersCite this book
- APA 7
- Abramson, J. (2021). Algebra and trigonometry 2e. OpenStax. https://openstax.org/books/algebra-and-trigonometry-2e/pages/1-introduction-to-prerequisites
- MLA 9
- Abramson, Jay. Algebra and Trigonometry 2e. OpenStax, 2021, https://openstax.org/books/algebra-and-trigonometry-2e/pages/1-introduction-to-prerequisites.
- Chicago author-date
- Abramson, Jay. 2021. Algebra and Trigonometry 2e. Houston, TX: OpenStax. https://openstax.org/books/algebra-and-trigonometry-2e/pages/1-introduction-to-prerequisites.
OpenStax entries are free to read online. Follow the licence shown on each linked source before redistributing or adapting its content.
Reuse the page responsiblyCite this pageAPA, MLA, Chicago, Harvard, BibTeX and RIS
These formats cite this calculator page itself. They are separate from the academic references above, which support the mathematical method and terminology.
APA 7
MW SysArc. (2026, July 21). Prime Number Checker. MW SysArc Tools. https://math.mwsysarc.com/algebra/prime-number-checker
MLA 9
MW SysArc. “Prime Number Checker.” MW SysArc Tools, 21 July 2026, https://math.mwsysarc.com/algebra/prime-number-checker. Accessed 31 Aug. 2026.
Chicago 17
MW SysArc. “Prime Number Checker.” MW SysArc Tools. Published July 21, 2026. Accessed August 31, 2026. https://math.mwsysarc.com/algebra/prime-number-checker.
Harvard
MW SysArc (2026) ‘Prime Number Checker’, MW SysArc Tools. Published 21 July 2026. Available at: https://math.mwsysarc.com/algebra/prime-number-checker (Accessed: 31 August 2026).
BibTeX and RIS records
BibTeX
@misc{mwsysarc_prime_check_2026,
author = {{MW SysArc}},
title = {Prime Number Checker},
howpublished = {MW SysArc Tools},
year = {2026},
url = {https://math.mwsysarc.com/algebra/prime-number-checker},
note = {Published July 21, 2026; accessed August 31, 2026}
}RIS
TY - ELEC
AU - MW SysArc
TI - Prime Number Checker
T2 - MW SysArc Tools
PY - 2026
DA - 2026-07-21
Y2 - 2026-08-31
UR - https://math.mwsysarc.com/algebra/prime-number-checker
N1 - Published July 21, 2026
ER -Clear answers
Frequently asked questions
What does the Prime checker do?
Determine whether a positive whole number is prime.
How does the Prime checker work?
The calculator applies Test divisors d≤√n. A composite number must have at least one factor no larger than its square root.
What can I learn from the Prime checker?
It connects the mathematical rule to your chosen numbers and shows each calculation step. Change one input at a time to see how the result responds.
Does MW SysArc receive or store what I enter?
No. The calculation runs locally in your browser. MW SysArc does not receive or store your calculation inputs.
How should I use the result?
Use the steps to understand the method, then verify important school or professional work using the notation and rounding rules required in your setting.
Last reviewed . Calculations tested .