The Number Dictionary

primitive Pythagorean Triples

A Pythagorean triple consists of three positive integers a, b, and c, such that a2 + b2 = c2.

Primitive Pythagorean Triple is a triple where a,b and c have no common factor.


Euclid (330-275 BC) gave a method for finding Pythagorean triple:
If λ, μ are natural numbers and λ> μ then x = λ2-μ2 , y = 2λμ,
z = λ2+μ2 is a Pythagorean triple.

Here we have a table with the first 100 Primitive Pythagorean Triples

Triple GeneratorsPythagorean Triangle SidesFactorized
num.λμxyzxyz
1213452 x 2
232512132 x 2 x 3
341158173 x 52 x 2 x 2
443724252 x 2 x 2 x 35 x 5
5522120293 x 72 x 2 x 5
654940413 x 32 x 2 x 2 x 5
7613512375 x 72 x 2 x 3
8651160612 x 2 x 3 x 5
9724528533 x 3 x 52 x 2 x 7
10743356653 x 112 x 2 x 2 x 75 x 13
11761384852 x 2 x 3 x 75 x 17
12816316653 x 3 x 72 x 2 x 2 x 25 x 13
13835548735 x 112 x 2 x 2 x 2 x 3
14853980893 x 132 x 2 x 2 x 2 x 5
1587151121133 x 52 x 2 x 2 x 2 x 7
16927736857 x 112 x 2 x 3 x 35 x 17
17946572975 x 132 x 2 x 2 x 3 x 3
1898171441452 x 2 x 2 x 2 x 3 x 35 x 29
1910199201013 x 3 x 112 x 2 x 5
2010391601097 x 132 x 2 x 3 x 5
21107511401493 x 172 x 2 x 5 x 7
22109191801812 x 2 x 3 x 3 x 5
23112117441253 x 3 x 132 x 2 x 115 x 5 x 5
24114105881373 x 5 x 72 x 2 x 2 x 11
25116851321575 x 172 x 2 x 3 x 11
26118571761853 x 192 x 2 x 2 x 2 x 115 x 37
271110212202213 x 72 x 2 x 5 x 1113 x 17
281211432414511 x 132 x 2 x 2 x 35 x 29
291251191201697 x 172 x 2 x 2 x 3 x 513 x 13
30127951681935 x 192 x 2 x 2 x 3 x 7
311211232642652 x 2 x 2 x 3 x 115 x 53
32132165521733 x 5 x 112 x 2 x 13
331341531041853 x 3 x 172 x 2 x 2 x 135 x 37
341361331562057 x 192 x 2 x 3 x 135 x 41
351381052082333 x 5 x 72 x 2 x 2 x 2 x 13
361310692602693 x 232 x 2 x 5 x 13
371312253123135 x 52 x 2 x 2 x 3 x 13
38141195281973 x 5 x 132 x 2 x 7
391431878420511 x 172 x 2 x 3 x 75 x 41
401451711402213 x 3 x 192 x 2 x 5 x 713 x 17
411491152522775 x 232 x 2 x 3 x 3 x 7
421411753083173 x 5 x 52 x 2 x 7 x 11
431413273643653 x 3 x 32 x 2 x 7 x 135 x 73
441522216022913 x 172 x 2 x 3 x 5
4515420912024111 x 192 x 2 x 2 x 3 x 5
461581612402897 x 232 x 2 x 2 x 2 x 3 x 517 x 17
471514294204212 x 2 x 3 x 5 x 7
48161255322573 x 5 x 172 x 2 x 2 x 2 x 2
491632479626513 x 192 x 2 x 2 x 2 x 2 x 35 x 53
501652311602813 x 7 x 112 x 2 x 2 x 2 x 2 x 5
511672072243053 x 3 x 232 x 2 x 2 x 2 x 2 x 75 x 61
521691752883375 x 5 x 72 x 2 x 2 x 2 x 2 x 3 x 3
5316111353523773 x 3 x 3 x 52 x 2 x 2 x 2 x 2 x 1113 x 29
541613874164253 x 292 x 2 x 2 x 2 x 2 x 135 x 5 x 17
551615314804812 x 2 x 2 x 2 x 2 x 3 x 513 x 37
56172285682933 x 5 x 192 x 2 x 17
571742731363053 x 7 x 132 x 2 x 2 x 175 x 61
5817625320432511 x 232 x 2 x 3 x 175 x 5 x 13
591782252723533 x 3 x 5 x 52 x 2 x 2 x 2 x 17
6017101893403893 x 3 x 3 x 72 x 2 x 5 x 17
6117121454084335 x 292 x 2 x 2 x 3 x 17
621714934764853 x 312 x 2 x 7 x 175 x 97
631716335445453 x 112 x 2 x 2 x 2 x 2 x 175 x 109
641813233632517 x 192 x 2 x 3 x 35 x 5 x 13
6518529918034913 x 232 x 2 x 3 x 3 x 5
661872752523735 x 5 x 112 x 2 x 3 x 3 x 7
6718112033964457 x 292 x 2 x 3 x 3 x 115 x 89
6818131554684935 x 312 x 2 x 3 x 3 x 1317 x 29
691817356126135 x 72 x 2 x 3 x 3 x 17
70192357763653 x 7 x 172 x 2 x 195 x 73
711943451523773 x 5 x 232 x 2 x 2 x 1913 x 29
721963252283975 x 5 x 132 x 2 x 3 x 19
731982973044253 x 3 x 3 x 112 x 2 x 2 x 2 x 195 x 5 x 17
7419102613804613 x 3 x 292 x 2 x 5 x 19
7519122174565057 x 312 x 2 x 2 x 3 x 195 x 101
7619141655325573 x 5 x 112 x 2 x 7 x 19
7719161056086173 x 5 x 72 x 2 x 2 x 2 x 2 x 19
781918376846852 x 2 x 3 x 3 x 195 x 137
79201399404013 x 7 x 192 x 2 x 2 x 5
8020339112040917 x 232 x 2 x 2 x 3 x 5
812073512804493 x 3 x 3 x 132 x 2 x 2 x 5 x 7
8220931936048111 x 292 x 2 x 2 x 3 x 3 x 513 x 37
8320112794405213 x 3 x 312 x 2 x 2 x 5 x 11
8420132315205693 x 7 x 112 x 2 x 2 x 5 x 13
8520171116806893 x 372 x 2 x 2 x 5 x 1713 x 53
862019397607613 x 132 x 2 x 2 x 5 x 19
872124378444519 x 232 x 2 x 3 x 75 x 89
882144251684575 x 5 x 172 x 2 x 2 x 3 x 7
8921837733650513 x 292 x 2 x 2 x 2 x 3 x 75 x 101
90211034142054111 x 312 x 2 x 3 x 5 x 7
9121161856726975 x 372 x 2 x 2 x 2 x 2 x 3 x 717 x 41
922120418408412 x 2 x 2 x 3 x 5 x 729 x 29
93221483444853 x 7 x 232 x 2 x 115 x 97
942234751324935 x 5 x 192 x 2 x 3 x 1117 x 29
952254592205093 x 3 x 3 x 172 x 2 x 5 x 11
962274353085333 x 5 x 292 x 2 x 7 x 1113 x 41
9722940339656513 x 312 x 2 x 3 x 3 x 115 x 113
9822133155726533 x 3 x 5 x 72 x 2 x 11 x 13
9922152596607097 x 372 x 2 x 3 x 5 x 11
10022171957487733 x 5 x 132 x 2 x 11 x 17


Cells with Dark blue background include prime numbers.
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