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A SPECIAL YEAR 2011

Posted by tendstoinfinity on January 13, 2011

I recently came across  Prof. Gary E. Davis‘s blog Republic of mathematics. He pointed out 2011 is itself a prime number and it can be represented as the sum of 11 consecutive prime numbers.

2011=157+163+167+173+179+181+191+193+197+199+211

or sum of 3 consecutiprime numbers 2011 = 661+673+677

The next year after 2011 that is a prime number and a sum of consecutive prime numbers is 2027 = 29+31+37+41+43+47+53+59+61+67+71+73+

79+83+89+97+101+103+107+109+113+127+131+137+139

but that year is not a sum of a prime number of consecutive prime numbers.

However, 2027 does have the curious and interesting property that it is prime and the sum of its digits 2+0+2+7=11 is also a prime number. It is the first year after 2003 that has this property.

The next year that is a prime number and a sum of a prime number of consecutive prime numbers is 2081 =401+409+419+421+431.

 


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