Why 7 is Weird - Numberphile

Divisible by 7 can be useful in figuring out if there is a whole number of weeks in a number of days.

this feels like a very old-school numberphile video, love it

For 40+ years I've been saying, "there is no rule for 7," meaning no way to check for divisibility as with 3, 5, 9 etc. Thank you for this. I now have my "rule for 7!"

The same algorithm (3:51) can be used to construct a formula for other primes: 11: x - y (k=10, j=99) 13: x + 4y or x - 9y (k=4, j=39) 17: x - 5y (k=12, j=119) 19: x + 2y (k=2, j=19) 23: x + 7y (k=7, j=69) 29: x + 3y (k=3, j=29) 31: x - 3y (k=28, j=279) 37: x - 11y (k=26, j=259) 41: x - 4y (k=37, j=369) 43: x + 13y or x - 30y (k=13, j=129) 47: x - 14y (k=33, j=329) 53: x + 16y (k=16, j=159) 59: x + 6y (k=6, j=59) 61: x - 6y (k=55, j=549) 67: x - 20y (k=47, j=469) 71: x - 7y (k=64, j=639) 73: x + 22y (k=22, j=219) 79: x + 8y (k=8, j=79) 83: x + 25y (k=25, j=249) 89: x + 9y (k=9, j=89) 97: x - 29y or x - 30x + x (k=68, j=679) where k is the multiplier of 10x + y: 10kx + ky (4:11) and j is a multiple of the prime that is subtracted: 10kx - jx + ky = x + ky (4:30) then subtract the prime if it helps And since the same algorithm is used, the results have the same properties, like iterability (1:24)

Seven is weird because it eight nine

When I was in the 7th grade, I was taught all the tests for divisibility except for 7. What we were told was "try dividing it by 7," which completely defeats the purpose of a divisibility test. Thank you for filling in this particular gap in my education.

Even Numberhile now recognizes the elegance of the number 7 Thala for a reason

One of the great things about youtube that is not talked about enough. There are so many creators I have watched for a decade or longer and they were so important to me and continue to be so. In the media too much attention is paid to the drama and such. What about people like this? Or the green brothers? Vsauce? Rhett and link? I could go on. It's not an easy thing to do, to be able to take your fans with you as they pass into different eras of their lives. Most adults don't still watch what they watched as kids but so many of us do with creators like I mentioned above. These people are my teachers and actually helped guide me to being a better adult. Me and so many others. It's a beautiful thing. The creators, as well as fellow followers, feel like family and it's such a comfort.

Can't believe that 10 years later, I am still loving watch James Grime on Numberphile. I watched him when I was a nerdy high schooler and now I'm a nerdy adult. Thank you so much for all the videos over the years.

another way to work out if something is divisible by 7 is to just do all your math in base 7 and see if it ends in 0

I always found multiples of 100, subtracted them and added on double the number of 100s you removed to what is remaining. Taking advantage of 98 being a multiple of 7. This works pretty well and is easy to do in your head

I’d always do it by comparing to other numbers. 7000 is divisible by 7, 7000-6468=532. If 532 is divisible by 7 then 6468 was. 700-532=168. 168-140=28. 28 is divisible by 7 so 6468 is. This method is much easier for me to do in my head because it’s only addition or subtraction.

I use divisibility for finding primes and root approximations during tutoring. I lacked the 7 test so, thanks for that!

Me and a friend of mine discovered a trick for 11 in middle school: Take 121, u split it in 1+21 = 22 so if the result is divisible by 11 the original is too. It works even for larger numbers like 35673 split in 3+56+73 = 132 132 split in 1+32 = 33 In case of even digits 1078 split in 10+78 = 88 Basically you split the number in sets of two digits starting from the end.

This is such a great video.. i’ve shared with my kids and the “presentation” with special british commentary and voice intonations is perfect. Useful and just enough entertainment!

The general rule for any number relatively prime with 10, call it p, is multiply the last digit by the multiplicative modular inverse of 10 mod p, and add the rest, and check the sum.

The most amazing thing about this video? James said "this weird trick" in the video, but that phrase doesn't appear in the title. Well done!

This video took me back in time, when I was a middle-schooler amazed by these tricks and properties of numbers. Even now in uni, I watch videos on this channel with the same flabbergasted look, enjoying every minute as an extraordinary discover. I really appreciate your content, you're doing great ✌️

Wow. I love this. I really love when the concept is abstracted out. Fantastic.

You have to love James Grime. Really! His passion, energy, and love for mathematics are just splashing on me from the monitor. Truly fantastic.👏 I wish I had such a passionate teacher/lecturer for my math lessons. I'm glad I could enjoy on YT for the least. 🙂