## 46002

46002^{2} = (1^{2} + 2)(3^{2} + 2)(11^{2} + 2)(24^{2} + 2)(30^{2} + 2) = (3^{2} + 2)(8^{2} + 2)(24^{2} + 2)(71^{2} + 2)

= (3^{2} + 2)(11^{2} + 2)(24^{2} + 2)(52^{2} + 2).

by Yoshio Mimura, Kobe, Japan

## 46054

46054^{2}± 3 are primes.

by Yoshio Mimura, Kobe, Japan

## 46064

46064^{2} = 321^{2} + 322^{2} + 323^{2} + 324^{2} + ... + 1856^{2}.

by Yoshio Mimura, Kobe, Japan

## 46070

46070^{2}± 3 are primes.

by Yoshio Mimura, Kobe, Japan

## 46080

328^{2} + 46080 = 392^{2}, 328^{2} - 46080 = 248^{2}.

46080^{2} = (2^{2} - 1)(3^{2} - 1)(5^{2} - 1)(7^{2} - 1)(9^{2} - 1)(31^{2} - 1).

by Yoshio Mimura, Kobe, Japan

## 46116

46116^{2} = (1^{2} + 5)(3^{2} + 5)(19^{2} + 5)(263^{2} + 5).

by Yoshio Mimura, Kobe, Japan

## 46125

46125^{2} = (4^{2} + 9)(6^{2} + 9)(14^{2} + 9)(96^{2} + 9).

by Yoshio Mimura, Kobe, Japan

## 46166

46166^{2} = 168^{2} + 169^{2} + 170^{2} + 171^{2} + ... + 1856^{2}.

by Yoshio Mimura, Kobe, Japan

## 46188

46188^{2}± 5 are primes.

46188^{2} = 2133331344, a square every digit of which is non-zero and smaller than 5.

by Yoshio Mimura, Kobe, Japan

## 46200

317^{2} + 46200 = 383^{2}, 317^{2} - 46200 = 233^{2}.

46200^{2} = (2^{2} - 1)(3^{2} - 1)(6^{2} - 1)(21^{2} - 1)(76^{2} - 1) = (2^{2} - 1)(76^{2} - 1)(351^{2} - 1)

= (3^{2} - 1)(4^{2} - 1)(6^{2} - 1)(21^{2} - 1)(34^{2} - 1) = (4^{2} - 1)(34^{2} - 1)(351^{2} - 1)

= (5^{2} - 1)(6^{2} - 1)(21^{2} - 1)(76^{2} - 1) = (6^{2} - 1)(11^{2} - 1)(21^{2} - 1)(34^{2} - 1)

= (21^{2} - 1)(29^{2} - 1)(76^{2} - 1).

by Yoshio Mimura, Kobe, Japan

## 46206

46206^{2}± 5 are primes.

by Yoshio Mimura, Kobe, Japan

## 46224

46224^{2} = (4^{2} + 8)(62^{2} + 8)(152^{2} + 8).

by Yoshio Mimura, Kobe, Japan

## 46230

46230^{2} = (14^{2} + 5)(15^{2} + 5)(215^{2} + 5).

by Yoshio Mimura, Kobe, Japan

## 46240

46240^{2} = (2^{2} + 4)(8^{2} + 4)(26^{2} + 4)(76^{2} + 4).

by Yoshio Mimura, Kobe, Japan

## 46250

46250^{2} = (2^{2} + 1)(7^{2} + 1)(43^{2} + 1)(68^{2} + 1).

by Yoshio Mimura, Kobe, Japan

## 46270

46270^{2}± 3 are primes.

by Yoshio Mimura, Kobe, Japan

## 46280

46280^{2} = (1^{2} + 4)(2^{2} + 4)(3^{2} + 4)(10^{2} + 4)(199^{2} + 4) = (3^{2} + 4)(6^{2} + 4)(10^{2} + 4)(199^{2} + 4).

by Yoshio Mimura, Kobe, Japan

## 46283

46283^{2} = 987^{2} + 988^{2} + 989^{2} + 990^{2} + ... + 1947^{2}.

by Yoshio Mimura, Kobe, Japan

## 46305

46305^{2} = 6524^{2} + 6525^{2} + 6526^{2} + 6526^{2} + ... + 6573^{2}.

by Yoshio Mimura, Kobe, Japan

## 46330

46330^{2}= 180 x 181 + 181 x 182 + 182 x 183 + 183 x 184 + ... + 1860 x 1861.

by Yoshio Mimura, Kobe, Japan

## 46389

46389^{2}± 2 are primes.

by Yoshio Mimura, Kobe, Japan

## 46400

46400^{2} = (1^{2} + 4)(2^{2} + 4)(6^{2} + 4)(14^{2} + 4)(82^{2} + 4) = (2^{2} + 4)(5^{2} + 4)(6^{2} + 4)(14^{2} + 4)(34^{2} + 4).

by Yoshio Mimura, Kobe, Japan

## 46425

46425^{2}± 2 are primes.

by Yoshio Mimura, Kobe, Japan

## 46431

46431^{2}± 2 are primes.

by Yoshio Mimura, Kobe, Japan

## 46464

220^{2} + 46464 = 308^{2}, 220^{2} - 46464 = 44^{2}.

by Yoshio Mimura, Kobe, Japan

## 46494

46494^{2} = (1^{2} + 5)(2^{2} + 5)(6^{2} + 5)(11^{2} + 5)(88^{2} + 5) = (1^{2} + 5)(4^{2} + 5)(6^{2} + 5)(7^{2} + 5)(88^{2} + 5)

= (1^{2} + 5)(4^{2} + 5)(47^{2} + 5)(88^{2} + 5) = (2^{2} + 5)(3^{2} + 5)(6^{2} + 5)(7^{2} + 5)(88^{2} + 5)

= (2^{2} + 5)(3^{2} + 5)(47^{2} + 5)(88^{2} + 5) = (2^{2} + 5)(4^{2} + 5)(6^{2} + 5)(11^{2} + 5)(47^{2} + 5)

= (6^{2} + 5)(7^{2} + 5)(11^{2} + 5)(88^{2} + 5) = (11^{2} + 5)(47^{2} + 5)(88^{2} + 5).

by Yoshio Mimura, Kobe, Japan

## 46504

46504^{2}± 3 are primes.

by Yoshio Mimura, Kobe, Japan

## 46512

46512^{2} = (2^{2} - 1)(5^{2} - 1)(18^{2} - 1)(305^{2} - 1) = (1^{2} + 8)(2^{2} + 8)(3^{2} + 8)(12^{2} + 8)(88^{2} + 8)

= (1^{2} + 8)(2^{2} + 8)(7^{2} + 8)(12^{2} + 8)(48^{2} + 8) = (1^{2} + 8)(12^{2} + 8)(14^{2} + 8)(88^{2} + 8)

= (1^{2} + 8)(12^{2} + 8)(26^{2} + 8)(48^{2} + 8) = (2^{2} + 8)(3^{2} + 8)(4^{2} + 8)(7^{2} + 8)(88^{2} + 8)

= (2^{2} + 8)(3^{2} + 8)(8^{2} + 8)(12^{2} + 8)(31^{2} + 8) = (2^{2} + 8)(4^{2} + 8)(31^{2} + 8)(88^{2} + 8)

= (2^{2} + 8)(7^{2} + 8)(20^{2} + 8)(88^{2} + 8) = (3^{2} + 8)(4^{2} + 8)(26^{2} + 8)(88^{2} + 8)

= (3^{2} + 8)(7^{2} + 8)(8^{2} + 8)(12^{2} + 8)(14^{2} + 8) = (3^{2} + 8)(10^{2} + 8)(12^{2} + 8)(88^{2} + 8)

= (3^{2} + 8)(12^{2} + 8)(14^{2} + 8)(64^{2} + 8) = (4^{2} + 8)(7^{2} + 8)(14^{2} + 8)(88^{2} + 8)

= (4^{2} + 8)(7^{2} + 8)(26^{2} + 8)(48^{2} + 8) = (7^{2} + 8)(10^{2} + 8)(12^{2} + 8)(48^{2} + 8)

= (8^{2} + 8)(12^{2} + 8)(14^{2} + 8)(31^{2} + 8) = (20^{2} + 8)(26^{2} + 8)(88^{2} + 8).

by Yoshio Mimura, Kobe, Japan

## 46526

46526^{2}± 3 are primes.

by Yoshio Mimura, Kobe, Japan

## 46536

46536^{2} = 2515 x 2516 + 2517 x 2518 + 2519 x 2520 + 2521 x 2522 + ... + 3067 x 3068.

by Yoshio Mimura, Kobe, Japan

## 46587

46587^{2} = 2170348569, a square with different digits.

by Yoshio Mimura, Kobe, Japan

## 46600

46600^{2} = (1^{2} + 4)(2^{2} + 4)(14^{2} + 4)(521^{2} + 4) = (6^{2} + 4)(14^{2} + 4)(521^{2} + 4).

by Yoshio Mimura, Kobe, Japan

## 46616

46616^{2}± 3 are primes.

by Yoshio Mimura, Kobe, Japan

## 46626

46626^{2}± 5 are primes.

by Yoshio Mimura, Kobe, Japan

## 46629

46629^{2}± 2 are primes.

by Yoshio Mimura, Kobe, Japan

## 46656

46656 = 216^{2}, a square with 3 kinds of digits.

by Yoshio Mimura, Kobe, Japan

## 46662

46662^{2} = (14^{2} + 6)(15^{2} + 6)(216^{2} + 6).

46662^{2}± 5 are primes.

by Yoshio Mimura, Kobe, Japan

## 46683

46683^{2} = (2^{2} - 1)(8^{2} - 1)(20^{2} - 1)(170^{2} - 1).

by Yoshio Mimura, Kobe, Japan

## 46684

46684^{2}± 3 are primes.

by Yoshio Mimura, Kobe, Japan

## 46728

46728^{2} = (1^{2} + 8)(13^{2} + 8)(16^{2} + 8)(72^{2} + 8) = (5^{2} + 8)(8^{2} + 8)(13^{2} + 8)(72^{2} + 8).

by Yoshio Mimura, Kobe, Japan

## 46732

46732^{2}± 3 are primes.

by Yoshio Mimura, Kobe, Japan

## 46800

46800^{2} = (4^{2} - 1)(9^{2} - 1)(1351^{2} - 1) = (4^{2} - 1)(11^{2} - 1)(14^{2} - 1)(79^{2} - 1)

= (4^{2} - 1)(14^{2} - 1)(17^{2} - 1)(51^{2} - 1) = (14^{2} - 1)(26^{2} - 1)(129^{2} - 1).

by Yoshio Mimura, Kobe, Japan

## 46818

46818^{2} = (1^{2} + 2)(4^{2} + 2)(24^{2} + 2)(265^{2} + 2) = (2^{2} + 2)(7^{2} + 2)(10^{2} + 2)(265^{2} + 2).

by Yoshio Mimura, Kobe, Japan

## 46822

4682246822 = 216385^{2}.

by Yoshio Mimura, Kobe, Japan

## 46830

46830^{2} = 10452 x 10453 + 10454 x 10455 + 10456 x 10457 + 10458 x 10459 + ... + 10490 x 10491.

by Yoshio Mimura, Kobe, Japan

## 46854

46854^{2} = (1^{2} + 2)(6^{2} + 2)(51^{2} + 2)(86^{2} + 2).

by Yoshio Mimura, Kobe, Japan

## 46862

46862^{2}± 3 are primes.

by Yoshio Mimura, Kobe, Japan

## 46880

46880^{2}± 3 are primes.

by Yoshio Mimura, Kobe, Japan

## 46886

46886^{2}± 3 are primes.

by Yoshio Mimura, Kobe, Japan

## 46893

46893^{2} = (1^{2} + 6)(9^{2} + 6)(15^{2} + 6)(125^{2} + 6).

by Yoshio Mimura, Kobe, Japan

## 46946

46946^{2}± 3 are primes.

by Yoshio Mimura, Kobe, Japan

## 46956

46956^{2} = (2^{2} + 3)(6^{2} + 3)(7^{2} + 3)(13^{2} + 3)(30^{2} + 3) = (2^{2} + 3)(13^{2} + 3)(30^{2} + 3)(45^{2} + 3)

= (6^{2} + 3)(13^{2} + 3)(19^{2} + 3)(30^{2} + 3).

by Yoshio Mimura, Kobe, Japan

## 46970

46970^{2}± 3 are primes.

by Yoshio Mimura, Kobe, Japan

## 46992

46992^{2} = 2208248064, a square with even digits.

46992^{2} = (6^{2} + 8)(16^{2} + 8)(436^{2} + 8).

by Yoshio Mimura, Kobe, Japan