## 29000

29000^{2} = (1^{2} + 4)(11^{2} + 4)(14^{2} + 4)(82^{2} + 4) = (1^{2} + 4)(5^{2} + 4)(6^{2} + 4)(11^{2} + 4)(34^{2} + 4)

= (5^{2} + 4)(11^{2} + 4)(14^{2} + 4)(34^{2} + 4).

by Yoshio Mimura, Kobe, Japan

## 29032

29032^{2}± 3 are primes.

by Yoshio Mimura, Kobe, Japan

## 29034

29034^{2} = 842973156 is a square with different digits.

by Yoshio Mimura, Kobe, Japan

## 29040

187^{2} + 29040 = 253^{2}, 187^{2} - 29040 = 77^{2}.

by Yoshio Mimura, Kobe, Japan

## 29049

29049^{2}± 2 are primes.

by Yoshio Mimura, Kobe, Japan

## 29084

29084^{2}± 3 are primes.

by Yoshio Mimura, Kobe, Japan

## 29085

29085^{2}± 2 are primes.

by Yoshio Mimura, Kobe, Japan

## 29094

29094^{2}± 5 are primes.

by Yoshio Mimura, Kobe, Japan

## 29106

29106^{2} = 847159236 is a square with different digits.

by Yoshio Mimura, Kobe, Japan

## 29140

29140^{2}= 192 x 193 + 193 x 194 + 194 x 195 +...+ 1366 x 1367.

by Yoshio Mimura, Kobe, Japan

## 29148

29148^{2}± 5 are primes.

by Yoshio Mimura, Kobe, Japan

## 29150

29150^{2} = (4^{2} + 6)(7^{2} + 6)(838^{2} + 6).

by Yoshio Mimura, Kobe, Japan

## 29186

29186^{2}± 3 are primes.

by Yoshio Mimura, Kobe, Japan

## 29200

29200^{2} = (1^{2} + 4)(2^{2} + 4)(4^{2} + 4)(19^{2} + 4)(54^{2} + 4) = (4^{2} + 4)(6^{2} + 4)(19^{2} + 4)(54^{2} + 4).

by Yoshio Mimura, Kobe, Japan

## 29208

29208^{2} = 853107264 is a square with different digits.

by Yoshio Mimura, Kobe, Japan

## 29241

29241 = 171^{2} is a zigzag square.

by Yoshio Mimura, Kobe, Japan

## 29250

29250^{2} = (1^{2} + 9)(2^{2} + 9)(4^{2} + 9)(21^{2} + 9)(24^{2} + 9) = (1^{2} + 9)(2^{2} + 9)(4^{2} + 9)(9^{2} + 9)(54^{2} + 9)

= (1^{2} + 9)(4^{2} + 9)(6^{2} + 9)(11^{2} + 9)(24^{2} + 9) = (1^{2} + 9)(54^{2} + 9)(171^{2} + 9)

= (15^{2} + 9)(24^{2} + 9)(79^{2} + 9) = (2^{2} + 9)(3^{2} + 9)(24^{2} + 9)(79^{2} + 9)

= (2^{2} + 9)(4^{2} + 9)(6^{2} + 9)(11^{2} + 9)(21^{2} + 9) = (2^{2} + 9)(4^{2} + 9)(9^{2} + 9)(171^{2} + 9)

= (2^{2} + 9)(6^{2} + 9)(15^{2} + 9)(79^{2} + 9) = (4^{2} + 9)(11^{2} + 9)(21^{2} + 9)(24^{2} + 9)

= (4^{2} + 9)(6^{2} + 9)(21^{2} + 9)(41^{2} + 9) = (4^{2} + 9)(9^{2} + 9)(11^{2} + 9)(54^{2} + 9).

by Yoshio Mimura, Kobe, Japan

## 29290

29290^{2} = (1^{2} + 4)(5^{2} + 4)(20^{2} + 4)(121^{2} + 4).

by Yoshio Mimura, Kobe, Japan

## 29325

29325^{2}± 2 are primes.

by Yoshio Mimura, Kobe, Japan

## 29337

29337^{2}± 2 are primes.

by Yoshio Mimura, Kobe, Japan

## 29372

29372^{2}± 3 are primes.

by Yoshio Mimura, Kobe, Japan

## 29380

29380^{2} = (1^{2} + 1)(3^{2} + 1)(15^{2} + 1)(437^{2} + 1).

by Yoshio Mimura, Kobe, Japan

## 29398

29398^{2} = 864242404 is a square with even digits.

by Yoshio Mimura, Kobe, Japan

## 29400

175^{2} + 29400 = 245^{2}, 175^{2} - 29400 = 35^{2}.

29400^{2} = (2^{2} - 1)(6^{2} - 1)(29^{2} - 1)(99^{2} - 1) = (4^{2} - 1)(6^{2} - 1)(13^{2} - 1)(99^{2} - 1).

29400^{2} = (1^{2} + 2^{3} + 3^{3} + ... + 7^{2})(8^{2} + 9^{2} + 10^{2})(11^{2} + 12^{3} + 13^{3} + ... + 42^{2}).

by Yoshio Mimura, Kobe, Japan

## 29404

29404^{2}± 3 are primes.

by Yoshio Mimura, Kobe, Japan

## 29409

29409^{2}± 2 are primes.

by Yoshio Mimura, Kobe, Japan

## 29410

29410^{2} = (13^{2} + 4)(2236^{2} + 4).

by Yoshio Mimura, Kobe, Japan

## 29412

29412^{2}± 5 are primes.

29412^{2} = (1^{2} + 2)(2^{2} + 2)(6^{2} + 2)(16^{2} + 2)(70^{2} + 2) = (4^{2} + 2)(6^{2} + 2)(16^{2} + 2)(70^{2} + 2).

by Yoshio Mimura, Kobe, Japan

## 29430

29430^{2} = (3^{2} + 9)(6^{2} + 9)(10^{2} + 9)(99^{2} + 9).

by Yoshio Mimura, Kobe, Japan

## 29432

29432^{2} = 866242624 is a square with even digits.

by Yoshio Mimura, Kobe, Japan

## 29463

29463^{2} = (38^{2} + 5)(774^{2} + 5) = (4^{2} + 5)(8^{2} + 5)(774^{2} + 5).

by Yoshio Mimura, Kobe, Japan

## 29493

29493^{2}± 2 are primes.

by Yoshio Mimura, Kobe, Japan

## 29575

29575^{2} = 106^{2} + 107^{2} + 108^{2} + ... + 1379^{2}.

by Yoshio Mimura, Kobe, Japan

## 29580

29580^{2} = (1^{2} + 9)(5^{2} + 9)(7^{2} + 9)(9^{2} + 9)(22^{2} + 9).

by Yoshio Mimura, Kobe, Japan

## 29584

29584 = 172^{2} is a square with different digits.

by Yoshio Mimura, Kobe, Japan

## 29592

29592^{2} = (4^{2} + 8)(35^{2} + 8)(172^{2} + 8).

by Yoshio Mimura, Kobe, Japan

## 29596

29596^{2} = (1^{2} + 3)(2^{2} + 3)(65^{2} + 3)(86^{2} + 3) = (5^{2} + 3)(65^{2} + 3)(86^{2} + 3).

by Yoshio Mimura, Kobe, Japan

## 29597

29597^{2} = 1595^{2} + 1596^{2} + 1597^{2} + ... + 1883^{2}.

by Yoshio Mimura, Kobe, Japan

## 29600

29600^{2} = (1^{2} + 4)(2^{2} + 4)(4^{2} + 4)(12^{2} + 4)(86^{2} + 4) = (2^{2} + 4)(6^{2} + 4)(12^{2} + 4)(136^{2} + 4)

= (4^{2} + 4)(6^{2} + 4)(12^{2} + 4)(86^{2} + 4).

by Yoshio Mimura, Kobe, Japan

## 29610

29610^{2} = (1^{2} + 5)(10^{2} + 5)(18^{2} + 5)(65^{2} + 5) = (18^{2} + 5)(25^{2} + 5)(65^{2} + 5)

= (4^{2} + 5)(5^{2} + 5)(18^{2} + 5)(65^{2} + 5) = (5^{2} + 5)(10^{2} + 5)(18^{2} + 5)(29^{2} + 5).

by Yoshio Mimura, Kobe, Japan

## 29614

29614^{2} = 876988996, a square every digit of which is greater than 5.

by Yoshio Mimura, Kobe, Japan

## 29624

29624^{2}± 3 are primes.

by Yoshio Mimura, Kobe, Japan

## 29626

29626^{2} = 877699876, a square every digit of which is greater than 5.

by Yoshio Mimura, Kobe, Japan

## 29646

29646^{2}± 5 are primes.

by Yoshio Mimura, Kobe, Japan

## 29696

29696^{2} = (3^{2} + 7)(11^{2} + 7)(15^{2} + 7)(43^{2} + 7).

by Yoshio Mimura, Kobe, Japan

## 29702

29702^{2} = 882208804 is a square with even digits.

by Yoshio Mimura, Kobe, Japan

## 29704

29704^{2}± 3 are primes.

by Yoshio Mimura, Kobe, Japan

## 29760

29760^{2} = (2^{2} - 1)(9^{2} - 1)(1921^{2} - 1).

481^{2} + 29760 = 511^{2}, 481^{2} - 29760 = 449^{2}.

by Yoshio Mimura, Kobe, Japan

## 29766

29766^{2} = (19^{2} + 2)(30^{2} + 2)(52^{2} + 2).

by Yoshio Mimura, Kobe, Japan

## 29770

29770^{2} = (1^{2} + 4)(3^{2} + 4)(15^{2} + 4)(244^{2} + 4) = (1^{2} + 9)(2^{2} + 9)(2611^{2} + 9) = (11^{2} + 9)(2611^{2} + 9).

by Yoshio Mimura, Kobe, Japan

## 29787

29787^{2}± 2 are primes.

by Yoshio Mimura, Kobe, Japan

## 29802

29802^{2} + 38868^{2} = 2398880628, mosaic.

by Yoshio Mimura, Kobe, Japan

## 29820

29820^{2} = 154*155*156 + 156*157*158 + 158*159*160 + 160*161*162 + ... + 294*295*296.

by Yoshio Mimura, Kobe, Japan

## 29822

29822^{2} = (7^{2} + 3)(20^{2} + 3)(206^{2} + 3).

by Yoshio Mimura, Kobe, Japan

## 29826

29826^{2}± 5 are primes.

by Yoshio Mimura, Kobe, Japan

## 29889

29889^{2} = (11^{2} + 2)(2695^{2} + 2).

by Yoshio Mimura, Kobe, Japan

## 29908

29908^{2}± 3 are primes.

by Yoshio Mimura, Kobe, Japan

## 29925

29925^{2}± 2 are primes.

by Yoshio Mimura, Kobe, Japan

## 29929

29929 = 173^{2} is a square with 2 kinds of digits.

by Yoshio Mimura, Kobe, Japan

## 29938

29938^{2}± 3 are primes.

by Yoshio Mimura, Kobe, Japan

## 29968

29968^{2}± 3 are primes.

by Yoshio Mimura, Kobe, Japan

## 29973

29973^{2}± 2 are primes.

by Yoshio Mimura, Kobe, Japan