2010
The factors of 2010 are: 1, 2, 3, 5, 6, 10, 15, 30, 67, 134, 201, 335, 402, 670, 1005, 2010
2 * 3 * 5 * 67 (Prime Factor Decomposition)
500 + 1000 + 500 + 5 + 5
19^2 + 25^2 + 32^2
2010 = 1 + 2 - (3 - 4 - 5)*6*7*8 - 9
2010 = 2*3*5*(7 + 11 + 13 + 17 + 19)
2010 = 2 x 3 x 5 x 67
2010 = 2 / 3 X 45 X 67
2345 * 6 / 7 = 2010
2010 = 0 - (1*2*3) + 4*567*8/9
36 * 57 - 42 = 2010
8*12*67*95 / 304 = 2010
0^7 + 1^9 + 2^8 + 3^6 + 4^5 = 2010
2*3*5*(7+11+13+17+19) = 2010
9+ 8*7 + 6*54*3*2 + 1 = 2010
2011
The factors of 2011 are: 1, 2011
The prime factors are: 2011 is a prime number.
1^7 + 1^9 + 2^8 + 3^6 + 4^5 = 2011
1 - (2 * 3) + ((4 * 567 * 8) / 9) = 2011
Using digits from 2 to 9 to get an expression equaling 2011 :
2011 = (2*((2 * 2 * 3 * 3 * 7)^2) - ((((2 * 3 * 3 * 7)^2) - ((5 * 5 * 5)^2))^2))^2 - (3 * 5 * ((2 * ((9^2) - (8^2)))^2) - (((7^2) - (4^2))^2))
Could you find other expressions?
2011 is also the sum of 11 CONSECUTIVE prime numbers: 2011=157+163+167+173+179+181+191+193+197+199+211
ReplyDeletevia @mathematicsprof (Twitter)
The previous prime number year was 2003, which is also a Lucas 8-step number
ReplyDeletehttp://mathworld.wolfram.com/Lucasn-StepNumber.html
2011 is also the sum of three consecutive prime numbers: 2011=661+673+677. So, 2011 is a prime number that can be expressed as the sum of consecutive prime numbers in 2 different ways!
ReplyDeleteWe can write 2011, using all 10 digits (0,1,..,9) and the basic arithmetic operations (+,-,*,/). Here are few examples:
ReplyDelete2011 = 670*3 + 1 + 2 + 4 + 8 - 9 - 5
2011 = 978 * 2 + 4 + 5 + 10 + 36
2011 = 2*47 + 3*89 + 1650
3 * 287 + 509 + 641, where all numbers used are prime numbers
Using one sign only: 2495 - 106 - 378 = 2011
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