2,916

[Math.]  Three square numbers using the same digits: 362 = 1,296, 542 = 2,916 and 962 = 9,216.

 

2,924

[Math.]  34×86 = 2,924 = 43×68.

 

[Math.]  A pair of amicable numbers (2620, 2924).

 

2,926

[Math.]  A triangular number (sum of all integers from 1 to 76):  2926 = 1+2+…+75+76.

 

2,927

[Math.]  A prime number, formed by 2 consecutive odd numbers. As is 2729.

 

2,937

[Math.]  The ratio 14685/2937 = 5, using each of 9 digits 1-9 once, shows how to arrange a 9-book set on 2 shelves to mark the book #5.

 

2,939

[Math.]  A right-truncatable prime number: self, 293, 29 and 2 are prime numbers.

 

2,943

[Math.]  Each ratio 17658/2943 = 27918/4653 = 34182/5697 = 6, using each of 9 digits 1-9 once, shows how to arrange a 9-book set on 2 shelves to mark the book #6.

 

2,964

[Math.]  The pair of numbers (2964, 2965) is called Smith brothers (consecutive Smith numbers).

 

2,967

[Math.]  The ratio 14835/2967 = 5, using each of 9 digits 1-9 once, shows how to arrange a 9-book set on 2 shelves to mark the book #5.

 

[Math.]  Two multiples of number 2967, 2967×5 = 14,835 and 2967×7 = 20,769, use each of 10 digits 0-9 once.

 

2,973

[Math.]  The ratio 14865/2973 = 5, using each of 9 digits 1-9 once, shows how to arrange a 9-book set on 2 shelves to mark the book #5.

 

2,991

[Math.]  j(2991) = 1992, where j is the Euler’s totient function.

 

2,996

[Math.]  2996 = 2222+99+9+666.

 

[Math.] 

296×333,667 = 98,765,432

2,996×33,336,667 = 99,876,654,332

29,996×3,333,366,667 = 99,987,666,543,332

299,996×333,333,666,667 = 99,998,766,665,433,332

...


2,997

[Math.]  2997 = 222+999+999+777.

 

[Math.] 

111,1113 = 1,371,737,997,260,631 and 1+371+737+997+260+631 = 3×999

222,2223 = 10,973,903,978,085,048 and 10+973+903+978+085+048 = 3×999

444,4443 = 87,791,231,824,680,384 and 87+791+231+824+680+384 = 3×999.

555,5553 = 171,467,249,657,578,875 and 171+467+249+657+578+875 = 3×999

888,8883 = 702,329,854,597,443,072 and 

                                                       702+329+854+597+443+072 = 3×999 = 2997.

 

2,999

[Math.]  Twin prime numbers: 2999 & 3001. Other: 29,999,999 and 30,000,001.

 

[Math.]  2999 = 2+999+999+999.