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41019

41019²± 2 are primes.

Page of Squares : First Upload March 5, 2014 ; Last Revised March 5, 2014
by Yoshio Mimura, Kobe, Japan

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41038

41039²± 3 are primes.

Page of Squares : First Upload March 5, 2014 ; Last Revised March 5, 2014
by Yoshio Mimura, Kobe, Japan

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41042

41042²± 3 are primes.

Page of Squares : First Upload March 5, 2014 ; Last Revised March 5, 2014
by Yoshio Mimura, Kobe, Japan

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41056

41056²± 3 are primes.

Page of Squares : First Upload March 5, 2014 ; Last Revised March 5, 2014
by Yoshio Mimura, Kobe, Japan

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41114

41114²± 3 are primes.

Page of Squares : First Upload March 5, 2014 ; Last Revised March 5, 2014
by Yoshio Mimura, Kobe, Japan

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41125

41125 ² = 1691265625, and 169 = 13², 1265625 = 1125².

Page of Squares : First Upload July 21, 2012 ; Last Revised July 21, 2012
by Yoshio Mimura, Kobe, Japan

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41127

41127²± 2 are primes.

Page of Squares : First Upload March 5, 2014 ; Last Revised March 5, 2014
by Yoshio Mimura, Kobe, Japan

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41139

41139²± 2 are primes.

Page of Squares : First Upload March 5, 2014 ; Last Revised March 5, 2014
by Yoshio Mimura, Kobe, Japan

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41160

259² + 41160 = 329², 259² - 41160 = 161²,
203² + 41160 = 287², 203² - 41160 = 7².

Page of Squares : First Upload July 21, 2012 ; Last Revised July 21, 2012
by Yoshio Mimura, Kobe, Japan

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41184

250² + 41184 = 322², 250² - 41184 = 146².

41184² = (2² - 1)(3² - 1)(12² - 1)(703² - 1) = (2² - 1)(7² - 1)(12² - 1)(287² - 1)
= (3² - 1)(5² - 1)(10² - 1)(12² - 1)(25² - 1) = (3² - 1)(12² - 1)(23² - 1)(53² - 1)
= (5² - 1)(12² - 1)(703² - 1) = (12² - 1)(53² - 1)(65² - 1).

Page of Squares : First Upload July 21, 2012 ; Last Revised March 5, 2014
by Yoshio Mimura, Kobe, Japan

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41209

41209 = 203², a zigzag square with different digita.

Page of Squares : First Upload July 21, 2012 ; Last Revised July 21, 2012
by Yoshio Mimura, Kobe, Japan

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41216

41216² = (1² + 7)(4² + 7)(7² + 7)(19² + 7)(21² + 7) = (3² + 7)(7² + 7)(21² + 7)(65² + 7)
= (4² + 7)(5² + 7)(7² + 7)(203² + 7) = (7² + 7)(27² + 7)(203² + 7).

Page of Squares : First Upload March 5, 2014 ; Last Revised March 5, 2014
by Yoshio Mimura, Kobe, Japan

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41225

41225 ² = 1699500625, and 16 = 4², 99500625 = 9975².

Page of Squares : First Upload July 21, 2012 ; Last Revised July 21, 2012
by Yoshio Mimura, Kobe, Japan

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41250

41250² = (2² + 6)(3² + 6)(7² + 6)(12² + 6)(37² + 6).

Page of Squares : First Upload March 5, 2014 ; Last Revised March 5, 2014
by Yoshio Mimura, Kobe, Japan

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41258

41258² = (2² + 3)(41² + 3)(380² + 3).

Page of Squares : First Upload March 5, 2014 ; Last Revised March 5, 2014
by Yoshio Mimura, Kobe, Japan

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41268

41268² = (4² + 3)(15² + 3)(627² + 3).

Page of Squares : First Upload March 5, 2014 ; Last Revised March 5, 2014
by Yoshio Mimura, Kobe, Japan

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41262

41262² = 3004 x 3005 + 3006 x 3007 + 3008 x 3009 + 3010 x 3011 + ... + 3340 x 3341.

Page of Squares : First Upload July 21, 2012 ; Last Revised July 21, 2012
by Yoshio Mimura, Kobe, Japan

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41290

41290²± 3 are primes.

Page of Squares : First Upload March 5, 2014 ; Last Revised March 5, 2014
by Yoshio Mimura, Kobe, Japan

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41323

(41323² +1 ) = (1² + 1)(2² + 1)(4² + 1)(6² + 1)(20² + 1)(26² + 1).

Page of Squares : First Upload July 21, 2012 ; Last Revised July 21, 2012
by Yoshio Mimura, Kobe, Japan

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41361

41361²± 2 are primes.

Page of Squares : First Upload March 5, 2014 ; Last Revised March 5, 2014
by Yoshio Mimura, Kobe, Japan

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41363

41363² = 1807² + 1809² + 1811² + 1813² + 1815² + ... + 2527².

Page of Squares : First Upload July 21, 2012 ; Last Revised July 21, 2012
by Yoshio Mimura, Kobe, Japan

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41376

41376² = 1711973376, a square with odd digits except the last digit 6.

Page of Squares : First Upload August 31, 2013 ; Last Revised August 31, 2013
by Yoshio Mimura, Kobe, Japan

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41382

41382² = (1² + 2)(2² + 2)(3² + 2)(6² + 2)(19² + 2)(25² + 2)
= (1² + 2)(2² + 2)(8² + 2)(19² + 2)(63² + 2) = (1² + 2)(3² + 2)(8² + 2)(14² + 2)(63² + 2)
= (1² + 2)(6² + 2)(8² + 2)(19² + 2)(25² + 2) = (2² + 2)(3² + 2)(4² + 2)(19² + 2)(63² + 2)
= (2² + 2)(14² + 2)(19² + 2)(63² + 2) = (3² + 2)(4² + 2)(6² + 2)(19² + 2)(25² + 2)
= (3² + 2)(6² + 2)(8² + 2)(13² + 2)(19² + 2) = (4² + 2)(8² + 2)(19² + 2)(63² + 2)
= (6² + 2)(14² + 2)(19² + 2)(25² + 2).

Page of Squares : First Upload March 5, 2014 ; Last Revised March 5, 2014
by Yoshio Mimura, Kobe, Japan

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41391

41391²± 2 are primes.

Page of Squares : First Upload March 5, 2014 ; Last Revised March 5, 2014
by Yoshio Mimura, Kobe, Japan

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41400

41400² = (2² - 1)(3² - 1)(4² - 1)(24² - 1)(91² - 1) = (2² - 1)(11² - 1)(24² - 1)(91² - 1)
= (4² - 1)(5² - 1)(24² - 1)(91² - 1) = (19² - 1)(24² - 1)(91² - 1) = (1² + 1)(2² + 1)(10² + 1)(1303² + 1)
= (1² + 1)(10² + 1)(32² + 1)(91² + 1) = (3² + 1)(10² + 1)(1303² + 1).

Page of Squares : First Upload March 5, 2014 ; Last Revised March 5, 2014
by Yoshio Mimura, Kobe, Japan

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41404

41404² = 2029² + 2030² + 2031² + 2032² + ... + 2380².

Page of Squares : First Upload July 21, 2012 ; Last Revised July 21, 2012
by Yoshio Mimura, Kobe, Japan

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41410

41410² = (1² + 1)(10² + 1)(32² + 1)(91² + 1)
= (1² + 1)(2² + 1)(10² + 1)(1303² + 1) = (3² + 1)(10² + 1)(1303² + 1).

Page of Squares : First Upload November 9, 2013 ; Last Revised November 9, 2013
by Yoshio Mimura, Kobe, Japan

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41414

41414² = 1715119396, a square with odd digits except the last digit 6.

Page of Squares : First Upload August 31, 2013 ; Last Revised August 31, 2013
by Yoshio Mimura, Kobe, Japan

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41442

41442²± 5 are primes.

Page of Squares : First Upload March 5, 2014 ; Last Revised March 5, 2014
by Yoshio Mimura, Kobe, Japan

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41444

41444²± 3 are primes.

Page of Squares : First Upload March 5, 2014 ; Last Revised March 5, 2014
by Yoshio Mimura, Kobe, Japan

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41454

41454² = (1² + 5)(2² + 5)(18² + 5)(311² + 5) = (1² + 5)(18² + 5)(29² + 5)(32² + 5)
= (4² + 5)(17² + 5)(18² + 5)(29² + 5) = (4² + 5)(29² + 5)(311² + 5) = (7² + 5)(18² + 5)(311² + 5).

Page of Squares : First Upload March 5, 2014 ; Last Revised March 5, 2014
by Yoshio Mimura, Kobe, Japan

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41490

41490² = (2² + 5)(5² + 5)(2525² + 5).

Page of Squares : First Upload March 5, 2014 ; Last Revised March 5, 2014
by Yoshio Mimura, Kobe, Japan

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41496

205² + 41496 = 289², 205² - 41496 = 23².

41496² = (1² + 3)(2² + 3)(3² + 3)(4² + 3)(7² + 3)(72² + 3)
= (1² + 3)(2² + 3)(4² + 3)(6² + 3)(15² + 3)(19² + 3) = (1² + 3)(2² + 3)(6² + 3)(9² + 3)(137² + 3)
= (1² + 3)(2² + 3)(7² + 3)(15² + 3)(72² + 3) = (1² + 3)(3² + 3)(4² + 3)(19² + 3)(72² + 3)
= (1² + 3)(4² + 3)(6² + 3)(23² + 3)(33² + 3) = (1² + 3)(4² + 3)(7² + 3)(9² + 3)(72² + 3)
= (1² + 3)(15² + 3)(19² + 3)(72² + 3) = (2² + 3)(3² + 3)(4² + 3)(6² + 3)(7² + 3)(23² + 3)
= (2² + 3)(3² + 3)(4² + 3)(23² + 3)(45² + 3) = (2² + 3)(3² + 3)(5² + 3)(6² + 3)(137² + 3)
= (2² + 3)(3² + 3)(33² + 3)(137² + 3) = (2² + 3)(4² + 3)(5² + 3)(6² + 3)(7² + 3)(15² + 3)
= (2² + 3)(4² + 3)(5² + 3)(15² + 3)(45² + 3) = (2² + 3)(4² + 3)(7² + 3)(15² + 3)(33² + 3)
= (2² + 3)(6² + 3)(7² + 3)(15² + 3)(23² + 3) = (2² + 3)(15² + 3)(23² + 3)(45² + 3)
= (3² + 3)(4² + 3)(5² + 3)(7² + 3)(72² + 3) = (3² + 3)(4² + 3)(6² + 3)(7² + 3)(61² + 3)
= (3² + 3)(4² + 3)(6² + 3)(19² + 3)(23² + 3) = (3² + 3)(4² + 3)(45² + 3)(61² + 3)
= (3² + 3)(7² + 3)(12² + 3)(137² + 3) = (3² + 3)(7² + 3)(15² + 3)(110² + 3)
= (3² + 3)(7² + 3)(23² + 3)(72² + 3) = (3² + 3)(9² + 3)(1307² + 3)
= (4² + 3)(5² + 3)(6² + 3)(15² + 3)(19² + 3) = (4² + 3)(6² + 3)(7² + 3)(9² + 3)(23² + 3)
= (4² + 3)(9² + 3)(23² + 3)(45² + 3) = (4² + 3)(15² + 3)(19² + 3)(33² + 3)
= (5² + 3)(6² + 3)(9² + 3)(137² + 3) = (5² + 3)(7² + 3)(15² + 3)(72² + 3)
= (6² + 3)(7² + 3)(15² + 3)(61² + 3) = (6² + 3)(15² + 3)(19² + 3)(23² + 3)
= (9² + 3)(33² + 3)(137² + 3) = (15² + 3)(45² + 3)(61² + 3) = (20² - 1)(27² - 1)(77² - 1).

Page of Squares : First Upload July 21, 2012 ; Last Revised March 5, 2014
by Yoshio Mimura, Kobe, Japan

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41524

41524²± 3 are primes.

Page of Squares : First Upload March 5, 2014 ; Last Revised March 5, 2014
by Yoshio Mimura, Kobe, Japan

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41544

41544² = (1² + 8)(8² + 8)(1632² + 8).

Page of Squares : First Upload March 5, 2014 ; Last Revised March 5, 2014
by Yoshio Mimura, Kobe, Japan

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41580

41580² = (2² - 1)(4² - 1)(8² - 1)(23² - 1)(34² - 1) = (2² - 1)(8² - 1)(9² - 1)(10² - 1)(34² - 1)
= (2² - 1)(8² - 1)(34² - 1)(89² - 1) = (2² - 1)(10² - 1)(34² - 1)(71² - 1) = (4² - 1)(10² - 1)(1079² - 1)
= (4² - 1)(6² - 1)(8² - 1)(10² - 1)(23² - 1) = (6² - 1)(8² - 1)(10² - 1)(89² - 1)
= (7² - 1)(8² - 1)(10² - 1)(76² - 1) = (10² - 1)(55² - 1)(76² - 1).

Page of Squares : First Upload March 5, 2014 ; Last Revised March 5, 2014
by Yoshio Mimura, Kobe, Japan

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41600

41600² = (2² + 4)(3² + 4)(4² + 4)(6² + 4)(10² + 4)(14² + 4)
= (2² + 4)(6² + 4)(10² + 4)(14² + 4)(16² + 4).

Page of Squares : First Upload March 5, 2014 ; Last Revised March 5, 2014
by Yoshio Mimura, Kobe, Japan

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41607

41607²± 2 are primes.

Page of Squares : First Upload March 5, 2014 ; Last Revised March 5, 2014
by Yoshio Mimura, Kobe, Japan

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41613

41613²± 2 are primes.

Page of Squares : First Upload March 5, 2014 ; Last Revised March 5, 2014
by Yoshio Mimura, Kobe, Japan

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41616

41616²± 5 are primes.

41616 = 204², a zigzag square pegged by 1.

41616² = (1² + 8)(2² + 8)(3² + 8)(20² + 8)(48² + 8) = (1² + 8)(3² + 8)(4² + 8)(14² + 8)(48² + 8)
= (3² + 8)(10² + 8)(20² + 8)(48² + 8) = (1² + 8)(14² + 8)(20² + 8)(48² + 8).

Page of Squares : First Upload July 21, 2012 ; Last Revised March 5, 2014
by Yoshio Mimura, Kobe, Japan

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41630

41630² = (15² + 5)(2745² + 5).

Page of Squares : First Upload March 5, 2014 ; Last Revised March 5, 2014
by Yoshio Mimura, Kobe, Japan

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41668

41668²± 3 are primes.

Page of Squares : First Upload March 5, 2014 ; Last Revised March 5, 2014
by Yoshio Mimura, Kobe, Japan

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41688

41688² = (4² + 8)(68² + 8)(125² + 8).

Page of Squares : First Upload March 5, 2014 ; Last Revised March 5, 2014
by Yoshio Mimura, Kobe, Japan

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41733

41733²± 2 are primes.

Page of Squares : First Upload March 5, 2014 ; Last Revised March 5, 2014
by Yoshio Mimura, Kobe, Japan

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41756

41756²± 3 are primes.

Page of Squares : First Upload March 5, 2014 ; Last Revised March 5, 2014
by Yoshio Mimura, Kobe, Japan

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41760

41760² = (3² - 1)(9² - 1)(28² - 1)(59² - 1).

Page of Squares : First Upload March 5, 2014 ; Last Revised March 5, 2014
by Yoshio Mimura, Kobe, Japan

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41770

41770²± 3 are primes.

Page of Squares : First Upload March 5, 2014 ; Last Revised March 5, 2014
by Yoshio Mimura, Kobe, Japan

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41796

41796² = (1² + 8)(10² + 8)(11² + 8)(118² + 8).

Page of Squares : First Upload March 5, 2014 ; Last Revised March 5, 2014
by Yoshio Mimura, Kobe, Japan

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41810

41810² = (4² + 4)(9349² + 4).

Page of Squares : First Upload March 5, 2014 ; Last Revised March 5, 2014
by Yoshio Mimura, Kobe, Japan

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41832

41832²± 5 are primes.

Page of Squares : First Upload March 5, 2014 ; Last Revised March 5, 2014
by Yoshio Mimura, Kobe, Japan

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41847

41847² = 1663² + 1664² + 1665² + 1666² + ... + 2143².

Page of Squares : First Upload July 21, 2012 ; Last Revised July 21, 2012
by Yoshio Mimura, Kobe, Japan

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41854

41854² = 1751757316, a square with odd digits except the last digit 6.

Page of Squares : First Upload August 31, 2013 ; Last Revised August 31, 2013
by Yoshio Mimura, Kobe, Japan

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41873

41873² = 2107² + 2108² + 2109² + 2109² + ... + 2444².

Page of Squares : First Upload July 21, 2012 ; Last Revised July 21, 2012
by Yoshio Mimura, Kobe, Japan

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41876

41876² = 1753599376, a square with odd digits except the last digit 6.

Page of Squares : First Upload August 31, 2013 ; Last Revised August 31, 2013
by Yoshio Mimura, Kobe, Japan

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41930

41930² = 3987 x 3988 + 3989 x 3990 + 3991 x 3992 + 3993 x 3994 + ... + 4195 x 4196.

Page of Squares : First Upload July 21, 2012 ; Last Revised July 21, 2012
by Yoshio Mimura, Kobe, Japan

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41959

1² + 2² + 3² + 4² + ... + 41959² = 24624626864860, which consists of even digits.

Page of Squares : First Upload July 21, 2012 ; Last Revised July 21, 2012
by Yoshio Mimura, Kobe, Japan

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