Prime Factorization (Displays Prime Factors and Exponents Side by Side) (Performance-Enhanced Version)
Author: hidekchi45Executions: 2184
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Prime Factorization (Displays Prime Factors and Exponents Side by Side) (Performance-Enhanced Version) Last Updated February 22, 2022
If prime factorization is possible, the result is always correct once the calculation is complete; however, the process is slow. If the number contains prime factors of 7 digits (1 million) or more, the calculation will either time out or be terminated. Please rest assured that it will not display false prime factorization results, such as those found in other “trial division” methods. A simplified version with reduced performance is also available.
○ 10-digit Mersenne prime M31: 2147483647 = 2^31－1
○ 12-digit Euclidean prime: 200560490131 = 31 × 29 × 23 × 19 × 17 × 13 × 11 × 7 × 5 × 3 × 2 + 1
○ 12-digit prime number: 999999000001 ✖ 14-digit prime number: 92709568269121 ✖ 16-digit prime number: 9007199254740997
✖ 19-digit Mersenne prime M61: 2305843009213693951 = 2^61 – 1
✖ 27-digit Mersenne prime M89: 618970019642690137449562111 = 2^89 − 1
✖33-digit Mersenne prime M107: 162259276829213363391578010288127 = 2^107 − 1
✖ 39-digit Mersenne prime M127: 170141183460469231731687303715884105727 = 2^127 − 1
==================== All of the following are composite numbers ====================
○ 51-digit: 664560874631152081456482432069736801730896106024103
△51 digits: 666070876152512717106070950186603615630383990358329
○ 48-digit: 996796498818862150784546058216343744333180483201
○ 21-digit Mersenne number M67: 147573952589676412927 = 2^67 − 1
△ 20-digit Mersenne number M65: 36893488147419103231 = 2^65 − 1
△ 20-digit Fermat number: 18446744073709551617
〇 19-digit Mersenne number M62: 4611686018427387903 = 2^62 − 1
○ 19-digit Mersenne number M63: 9223372036854775807 = 2^63 − 1
〇19-digit Mersenne number M64: 18446744073709551615 = 2^64 − 1
〇16-digit: 8635844967113809 = 89652331 × 96325939
〇13-digit: 1565912117761 = 1162193 × 1347377
〇19!: 121645100408832000 〇20!: 2432902008176640000 〇21!: 51090942171709440000
〇16!: 20922789888000 〇17!: 355687428096000 〇18!: 6402373705728000
515377520732011331036461129765621272702107522001 = 3^100 125129118027271453 =277^7
〇4653951142058652573197980505065592149562928915510 〇5000009111777111
〇2341695598348007663 〇123456789012345678901 〇16 digits:1111111111111111 〇24001460029100189
〇17 digits: 99999999999999999
○ 10-digit Mersenne prime M31: 2147483647 = 2^31－1
○ 12-digit Euclidean prime: 200560490131 = 31 × 29 × 23 × 19 × 17 × 13 × 11 × 7 × 5 × 3 × 2 + 1
○ 12-digit prime number: 999999000001 ✖ 14-digit prime number: 92709568269121 ✖ 16-digit prime number: 9007199254740997
✖ 19-digit Mersenne prime M61: 2305843009213693951 = 2^61 – 1
✖ 27-digit Mersenne prime M89: 618970019642690137449562111 = 2^89 − 1
✖33-digit Mersenne prime M107: 162259276829213363391578010288127 = 2^107 − 1
✖ 39-digit Mersenne prime M127: 170141183460469231731687303715884105727 = 2^127 − 1
==================== All of the following are composite numbers ====================
○ 51-digit: 664560874631152081456482432069736801730896106024103
△51 digits: 666070876152512717106070950186603615630383990358329
○ 48-digit: 996796498818862150784546058216343744333180483201
○ 21-digit Mersenne number M67: 147573952589676412927 = 2^67 − 1
△ 20-digit Mersenne number M65: 36893488147419103231 = 2^65 − 1
△ 20-digit Fermat number: 18446744073709551617
〇 19-digit Mersenne number M62: 4611686018427387903 = 2^62 − 1
○ 19-digit Mersenne number M63: 9223372036854775807 = 2^63 − 1
〇19-digit Mersenne number M64: 18446744073709551615 = 2^64 − 1
〇16-digit: 8635844967113809 = 89652331 × 96325939
〇13-digit: 1565912117761 = 1162193 × 1347377
〇19!: 121645100408832000 〇20!: 2432902008176640000 〇21!: 51090942171709440000
〇16!: 20922789888000 〇17!: 355687428096000 〇18!: 6402373705728000
515377520732011331036461129765621272702107522001 = 3^100 125129118027271453 =277^7
〇4653951142058652573197980505065592149562928915510 〇5000009111777111
〇2341695598348007663 〇123456789012345678901 〇16 digits:1111111111111111 〇24001460029100189
〇17 digits: 99999999999999999
I suspect that the prime factorization feature provided by Casio likely uses a different CPU allocation; since this was created within the scope of features intended for general users, it is completely outclassed by the Casio version in terms of performance.Since the Casio version doesn’t display prime factors in exponential notation, this version provides a clearer presentation of the results. Additionally, the ability to perform prime factorization on numbers up to 51 digits is an advantage over the Casio version.
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