834 is the sum of consecutive prime numbers two different ways:

- 127 + 131 + 137 + 139 + 149 + 151 = 834; that’s six consecutive primes
- 31 + 37 + 41 + 43 + 47 + 53 + 59 + 61 + 67 + 71 + 73 + 79 + 83 + 89 = 834; that’s fourteen consecutive primes

The ONLY Pythagorean triple that contains the number 834 is 834 – 173888 – 173890.

- 834 is a composite number.
- Prime factorization: 834 = 2 × 3 × 139
- The exponents in the prime factorization are 1, 1, and 1. Adding one to each and multiplying we get (1 + 1)(1 + 1)(1 + 1) = 2 × 2 × 2 = 8. Therefore 834 has exactly 8 factors.
- Factors of 834: 1, 2, 3, 6, 139, 278, 417, 834
- Factor pairs: 834 = 1 × 834, 2 × 417, 3 × 278, or 6 × 139
- 834 has no square factors that allow its square root to be simplified. √834 ≈ 28.879058

There was a solar eclipse in the United States today. People where I lived were able to experience 91.32% obstruction of the sun. I love this interactive map of today’s eclipse and past and future ones as well.

Several people have taken and shared marvelous pictures of the eclipse.

Here are a few tweets I saw about eclipses on twitter:

Solar eclipse. Source: https://t.co/4t0LT1Gd6I pic.twitter.com/goXUDCOvuj

— Cliff Pickover (@pickover) August 20, 2017

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Lunar eclipse. Solar eclipse… #SolarEclipse2017 pic.twitter.com/uZ7vCmv2DI

— Cliff Pickover (@pickover) August 21, 2017

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#SolarEclipse2017 as seen through a saltine cracker. pic.twitter.com/BVPDB24cTC

— Megan Wilson-Reitz (@WilsonReitz) August 21, 2017

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Are your kids ready for this free #SolarEclipse2017 math puzzle? https://t.co/Uu8tEMh9an #MTBoS #iteachmath pic.twitter.com/aN0egwDiAO

— Mashup Math (@mashupmath) August 21, 2017

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Just took this photo of the #SolarEclipse2017 pic.twitter.com/P9UmkcyEra

— Holly (@hollyhaygood) August 21, 2017

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