3,300

[EECS]  3.3K(W) is one of standard numerical values for resistors (of tolerance class 5%). 3,300mF (microfarads) is one of standard numerical values for capacitors.

 

3,311

[Math.]  A pyramidal number (sum of all squares of integers from 1 to 21): 3311 = 12+22+…+202+212.

 

3,313

[Math.]  A prime number.  The smallest prime whose digit n appears n times.

 

[Math.]  A pair of prime numbers (p = 17, q = 3313) found by Stephens (1971), that 2 numbers of the form (pq–1)/(p–1) and (qp–1)/(q–1) have a common prime factor 112643, as a counter-example to the Feit-Thompson conjecture that no such pair of prime numbers could exist.

 

3,321

[Math.]  A triangular number (sum of all integers from 1 to 81): 3321 = 1+2+…+80+81.

 

3,322

[Sport]  One of soccer’s possible lineup tactics formations: 3-3-4 (3 defenders, 3 midfielders and 4 forwards). A slightly modified forwards line makes: 3-3-3-1 (1 striker) or 3-3-2-2 (2 strikers).

 

3,331

[Math.]  A prime number, formed by 3 adjacent digits 3 and 1 digit 1.  A prime whose digit n appears n times.

 

[Sport]  One of soccer’s possible lineup tactics formations: 3-3-4 (3 defenders, 3 midfielders and 4 forwards). A slightly modified forwards line makes: 3-3-3-1 (1 striker) or 3-3-2-2 (2 strikers).

 

3332

[Math.]  Square of numbers of similar pattern xxy, where y = x–1.

* 1102 = 012,100 & 012+100 = 112 = 110+2.

* 3322 = 110,224 & 110+224 = 334 = 332+2.

3332= 11,102,224 & 1,110+2,224 = 3,334 = 3,332+2.

Similarly, 3…322 = 1…102…24 & 1…10+2…24 = 3…34 = 3…32+2.

* 4432 = 196,249 & 196+249 = 445 = 443+2

* 6652 = 442,225 & 442+225 = 667 = 665+2.

Similarly, 6…652 = 4…422…25 & 4…42+2…25 = 6…67 = 6…65+2.

* 7762 = 602,176 & 602+176 = 778 = 776+2.

 

3333, 3334, 3335, 3336, 3337, 3,347 & 3,357

[Math.] 

33×34 = 1122

33×35 = 1155

33×36 = 1188

33×37 = 1221

33×47 = 1551

33×57 = 1881

 ...

 

3333×3334 = 11112222

3333×3335 = 11115555

3333×3336 = 11118888

3333×3337 = 11122221

3333×3347 = 11155551

3333×3357 = 11188881

… (generalizable pattern) …

 

3,333

[Math.]  333,366,670,000 = 33333+66673+00003.

333,366,670,001 = 33333+66673+00013.

166,650,003,333 = 16663+50003+33333.

1,000,000,166,650,003,333 = 10000003+16663+50003+33333. (Generalizable)

  

[Phone]  The number to key in text messaging on telephone keypad for number 3.

 

3,333 & 3,367

 [Math.]

3×37 = 111

33×3367 = 111,111

333×333667 = 111,111,111

3333×33336667 = 111,111,111,111

33333×3333366667 = 111,111,111,111,111

 

3,334

[Math.]  33,346,668 = 66682–33342 = (3334+6668)×3334, where 6668 = 3334×2.

 

333,400,006,667 = 33343+00003+66673 and

333,401,006,667 = 33343+01003+66673.  (Generalizable)

 

[Math.]  Repeatedly inserting numbers 15 in the middle of the square number 16 yields other squares 1156 = 342, 111556 = 3342, 11115556 = 33342

 

3,335

[Math.]  Repeatedly inserting numbers 12 between the digits 1 and 2 in the square number 1225 = 352 yields other squares 112225 = 3352, 11122225 = 33352, 1111222225 = 333352

 

3,340

[Math.]  3340 = 3333+3+4+0.

3341 = 3333+3+4+1.

3342 = 3333+3+4+2.

3343 = 3333+3+4+3. A prime number.

3344 = 3333+3+4+4.

3345 = 3333+3+4+5.

3346 = 3333+3+4+6.

3347 = 3333+3+4+7. A prime number.

3348 = 3333+3+4+8.

3349 = 3333+3+4+9.

 

3,347 & 3,357 (See more above)

 

3,364

[Math.]  3364 = (–3–3+64)2 = 582.

 

3,367

[Math.]  372 = 1369 = 1368+1

33672 = 11336689 = 11336688+1

333,6672 = 111,333,666,889 = 111,333,666,888+1

...

 

3,379

[Math.]  Square and cube of number 3379 use different digits: 33792 = 11,417,641 and 33793 = 38,580,208,939.