---

58000

58000² = (1² + 4)(2² + 4)(4² + 4)(5² + 4)(11² + 4)(34² + 4)
= (1² + 4)(2² + 4)(5² + 4)(6² + 4)(11² + 4)(24² + 4) = (1² + 4)(2² + 4)(11² + 4)(24² + 4)(34² + 4)
= (1² + 4)(4² + 4)(6² + 4)(11² + 4)(82² + 4) = (2² + 4)(5² + 4)(11² + 4)(14² + 4)(24² + 4)
= (4² + 4)(5² + 4)(6² + 4)(11² + 4)(34² + 4) = (4² + 4)(11² + 4)(14² + 4)(82² + 4)
= (6² + 4)(11² + 4)(24² + 4)(34² + 4).

Page of Squares : First Upload March 19, 2014 ; Last Revised March 19, 2014
by Yoshio Mimura, Kobe, Japan

---

58050

58050² = 316² + 317² + 318² + ... + 2164².

Page of Squares : First Upload September 22, 2012 ; Last Revised September 22, 2012
by Yoshio Mimura, Kobe, Japan

---

58065

58065² = (1² + 6)(3² + 6)(27² + 6)(209² + 6).

Page of Squares : First Upload March 19, 2014 ; Last Revised March 19, 2014
by Yoshio Mimura, Kobe, Japan

---

58066

58066²± 3 are primes.

Page of Squares : First Upload March 19, 2014 ; Last Revised March 19, 2014
by Yoshio Mimura, Kobe, Japan

---

58076

58076²± 3 are primes.

Page of Squares : First Upload March 19, 2014 ; Last Revised March 19, 2014
by Yoshio Mimura, Kobe, Japan

---

58080

286² + 58080 = 374², 286² - 58080 = 154².

Page of Squares : First Upload September 22, 2012 ; Last Revised September 22, 2012
by Yoshio Mimura, Kobe, Japan

---

58081

58081 = 241² is a zigzag square pegged by 8.

Page of Squares : First Upload September 22, 2012 ; Last Revised September 22, 2012
by Yoshio Mimura, Kobe, Japan

---

58082

58082² = (15² + 1)(16² + 1)(241² + 1).

Page of Squares : First Upload November 16, 2013 ; Last Revised November 16, 2013
by Yoshio Mimura, Kobe, Japan

---

58116

58116²± 5 are primes.

Page of Squares : First Upload March 19, 2014 ; Last Revised March 19, 2014
by Yoshio Mimura, Kobe, Japan

---

58120

58120²± 3 are primes.

Page of Squares : First Upload March 19, 2014 ; Last Revised March 19, 2014
by Yoshio Mimura, Kobe, Japan

---

58146

58146² = (3² + 2)(8² + 2)(2158² + 2).

Page of Squares : First Upload March 19, 2014 ; Last Revised March 19, 2014
by Yoshio Mimura, Kobe, Japan

---

58167

58167² = 3383399889 is a square with 3 kinds of digits.

Page of Squares : First Upload September 22, 2012 ; Last Revised September 22, 2012
by Yoshio Mimura, Kobe, Japan

---

58201

58201 = 132⁴ + 165⁴ + 220⁴.

Page of Squares : First Upload September 22, 2012 ; Last Revised September 22, 2012
by Yoshio Mimura, Kobe, Japan

---

58240

58240² = (3² - 1)(6² - 1)(27² - 1)(129² - 1) = (3² - 1)(15² - 1)(27² - 1)(51² - 1).

Page of Squares : First Upload March 19, 2014 ; Last Revised March 19, 2014
by Yoshio Mimura, Kobe, Japan

---

58242

58242² = (2² + 2)(24² + 2)(989² + 2).

Page of Squares : First Upload March 19, 2014 ; Last Revised March 19, 2014
by Yoshio Mimura, Kobe, Japan

---

58250

58250² = (1² + 4)(4² + 4)(11² + 4)(521² + 4).

Page of Squares : First Upload March 19, 2014 ; Last Revised March 19, 2014
by Yoshio Mimura, Kobe, Japan

---

58263

58263²± 2 are primes.

Page of Squares : First Upload March 19, 2014 ; Last Revised March 19, 2014
by Yoshio Mimura, Kobe, Japan

---

58320

369² + 58320 = 441², 369² - 58320 = 279².

Page of Squares : First Upload September 22, 2012 ; Last Revised September 22, 2012
by Yoshio Mimura, Kobe, Japan

---

58344

58344²± 5 are primes.

Page of Squares : First Upload March 19, 2014 ; Last Revised March 19, 2014
by Yoshio Mimura, Kobe, Japan

---

58394

58394² = (2² + 3)(26² + 3)(847² + 3).

Page of Squares : First Upload March 19, 2014 ; Last Revised March 19, 2014
by Yoshio Mimura, Kobe, Japan

---

58413

58413² = 3412078569 is a square with different digits.

Page of Squares : First Upload September 22, 2012 ; Last Revised September 22, 2012
by Yoshio Mimura, Kobe, Japan

---

58455

58455² = 3416987025 is a square with different digits.

Page of Squares : First Upload September 22, 2012 ; Last Revised September 22, 2012
by Yoshio Mimura, Kobe, Japan

---

58464

58464² = (3² - 1)(13² - 1)(28² - 1)(57² - 1).

Page of Squares : First Upload March 19, 2014 ; Last Revised March 19, 2014
by Yoshio Mimura, Kobe, Japan

---

58476

58476² = (2² + 8)(42² + 8)(401² + 8).

Page of Squares : First Upload March 19, 2014 ; Last Revised March 19, 2014
by Yoshio Mimura, Kobe, Japan

---

58500

58500² = (1² + 9)(2² + 9)(3² + 9)(4² + 9)(11² + 9)(21² + 9)
= (1² + 9)(2² + 9)(3² + 9)(15² + 9)(79² + 9) = (1² + 9)(3² + 9)(4² + 9)(21² + 9)(41² + 9)
= (1² + 9)(4² + 9)(11² + 9)(15² + 9)(21² + 9) = (1² + 9)(9² + 9)(11² + 9)(171² + 9)
= (3² + 9)(11² + 9)(15² + 9)(79² + 9).

Page of Squares : First Upload March 19, 2014 ; Last Revised March 19, 2014
by Yoshio Mimura, Kobe, Japan

---

58538

58538²± 3 are primes.

Page of Squares : First Upload March 19, 2014 ; Last Revised March 19, 2014
by Yoshio Mimura, Kobe, Japan

---

58554

58554² = 3428570916 is a square with different digits.

Page of Squares : First Upload September 22, 2012 ; Last Revised September 22, 2012
by Yoshio Mimura, Kobe, Japan

---

58557

58557²± 2 are primes.

Page of Squares : First Upload March 19, 2014 ; Last Revised March 19, 2014
by Yoshio Mimura, Kobe, Japan

---

58564

58564 = 242² is a zigzag sqaure.

Page of Squares : First Upload September 22, 2012 ; Last Revised September 22, 2012
by Yoshio Mimura, Kobe, Japan

---

58565

58565² = (8² + 1)(30² + 1)(242² + 1).

Page of Squares : First Upload November 16, 2013 ; Last Revised November 16, 2013
by Yoshio Mimura, Kobe, Japan

---

58566

58566² = (15² + 2)(16² + 2)(242² + 2).

Page of Squares : First Upload March 19, 2014 ; Last Revised March 19, 2014
by Yoshio Mimura, Kobe, Japan

---

58569

The quadratic polynomial 58569X² - 185262X + 232969 takes the values 326², 311², 452², 655², 878², 1109² at X = 1, 2,..., 6.

Page of Squares : First Upload September 22, 2012 ; Last Revised September 22, 2012
by Yoshio Mimura, Kobe, Japan

---

58575

58575² = (4² - 1)(15124² - 1).

Page of Squares : First Upload March 19, 2014 ; Last Revised March 19, 2014
by Yoshio Mimura, Kobe, Japan

---

58578

58578²± 5 are primes.

Page of Squares : First Upload March 19, 2014 ; Last Revised March 19, 2014
by Yoshio Mimura, Kobe, Japan

---

58580

58580² = (4² + 4)(5² + 4)(20² + 4)(121² + 4) = (20² + 4)(24² + 4)(121² + 4).

Page of Squares : First Upload March 19, 2014 ; Last Revised March 19, 2014
by Yoshio Mimura, Kobe, Japan

---

58612

58612²± 3 are primes.

Page of Squares : First Upload March 19, 2014 ; Last Revised March 19, 2014
by Yoshio Mimura, Kobe, Japan

---

58628

58628²± 3 are primes.

Page of Squares : First Upload March 19, 2014 ; Last Revised March 19, 2014
by Yoshio Mimura, Kobe, Japan

---

58660

58660² = 2437 x 2438 + 2439 x 2440 + 2441 x 2442 + 2443 x 2444 + ... + 3273 x 3274.

Page of Squares : First Upload September 22, 2012 ; Last Revised September 22, 2012
by Yoshio Mimura, Kobe, Japan

---

58722

58722² + 45138² = 5485712328, a mosaic.

Page of Squares : First Upload September 22, 2012 ; Last Revised September 22, 2012
by Yoshio Mimura, Kobe, Japan

---

58760

58760² = (1² + 4)(2² + 4)(30² + 4)(309² + 4) = (1² + 4)(30² + 4)(874² + 4)
= (6² + 4)(30² + 4)(309² + 4).

Page of Squares : First Upload March 19, 2014 ; Last Revised March 19, 2014
by Yoshio Mimura, Kobe, Japan

---

58764

58764²± 5 are primes.

58764² = (2² + 8)(18² + 8)(931² + 8).

Page of Squares : First Upload March 19, 2014 ; Last Revised March 19, 2014
by Yoshio Mimura, Kobe, Japan

---

58800

58800² = (2² - 1)(4² - 1)(6² - 1)(15² - 1)(99² - 1).

Page of Squares : First Upload March 19, 2014 ; Last Revised March 19, 2014
by Yoshio Mimura, Kobe, Japan

---

58806

58806² = (1² + 2)(2² + 2)(5² + 2)(19² + 2)(140² + 2) = (1² + 2)(3² + 2)(5² + 2)(14² + 2)(140² + 2)
= (3² + 2)(5² + 2)(8² + 2)(19² + 2)(22² + 2) = (4² + 2)(5² + 2)(19² + 2)(140² + 2)
= (19² + 2)(22² + 2)(140² + 2).

Page of Squares : First Upload March 19, 2014 ; Last Revised March 19, 2014
by Yoshio Mimura, Kobe, Japan

---

58821

58821²± 2 are primes.

Page of Squares : First Upload March 19, 2014 ; Last Revised March 19, 2014
by Yoshio Mimura, Kobe, Japan

---

58824

58824² = (1² + 8)(11² + 8)(12² + 8)(140² + 8) = (4² + 8)(7² + 8)(11² + 8)(140² + 8).

Page of Squares : First Upload March 19, 2014 ; Last Revised March 19, 2014
by Yoshio Mimura, Kobe, Japan

---

58833

58833²± 2 are primes.

Page of Squares : First Upload March 19, 2014 ; Last Revised March 19, 2014
by Yoshio Mimura, Kobe, Japan

---

58854

58854² = (7² + 2)(10² + 2)(816² + 2).

Page of Squares : First Upload March 19, 2014 ; Last Revised March 19, 2014
by Yoshio Mimura, Kobe, Japan

---

58870

58870² = (38² + 6)(1546² + 6).

Page of Squares : First Upload March 19, 2014 ; Last Revised March 19, 2014
by Yoshio Mimura, Kobe, Japan

---

58905

58905² = (4² - 1)(8² - 1)(16² - 1)(120² - 1).

Page of Squares : First Upload March 19, 2014 ; Last Revised March 19, 2014
by Yoshio Mimura, Kobe, Japan

---

58916

58916²± 3 are primes.

Page of Squares : First Upload March 19, 2014 ; Last Revised March 19, 2014
by Yoshio Mimura, Kobe, Japan

---

58926

58926² = (1² + 5)(3² + 5)(8² + 5)(774² + 5) = (1² + 5)(31² + 5)(774² + 5).

Page of Squares : First Upload March 19, 2014 ; Last Revised March 19, 2014
by Yoshio Mimura, Kobe, Japan

---