Tim's Collaborative Padlet by https://padlet.com/tclark208/wvc33tfi4eamyjpb For students to post ideas ... en-us 2023-06-07 08:17:09 UTC 2023-06-08 17:13:33 UTC hello@padlet.com https://padlet.net/icons/png/1f3b8.png Tim's first generalisation tclark208 https://padlet.com/tclark208/wvc33tfi4eamyjpb/wish/2617329841 Many of you found empirically that the longest run of consecutive composite numbers in the set 1-500 was length 13.

Generalising, can I determine the length of the longest run in a set 1-n?  ]]> 2023-06-07 16:47:26 UTC https://padlet.com/tclark208/wvc33tfi4eamyjpb/wish/2617329841 Tim's investigation idea tclark208 https://padlet.com/tclark208/wvc33tfi4eamyjpb/wish/2617331501 How many runs of m (consecutive composite numbers) are there in the set 1-500?

(... and so, immediately following, in the set 1-n?)]]> 2023-06-07 16:49:08 UTC https://padlet.com/tclark208/wvc33tfi4eamyjpb/wish/2617331501 room 1 0418jenny https://padlet.com/tclark208/wvc33tfi4eamyjpb/wish/2618492021 Conjecture: prime numbers are spread unevenly in an interval.
Further investigation: Can we work backwards from the run of non prime number to expressing it in a generating function?]]> 2023-06-08 17:01:47 UTC https://padlet.com/tclark208/wvc33tfi4eamyjpb/wish/2618492021 Group 4's investigation idea https://padlet.com/tclark208/wvc33tfi4eamyjpb/wish/2618495005 How many groups of three consecutive non-prime numbers are there from 1-500?


]]> 2023-06-08 17:06:59 UTC https://padlet.com/tclark208/wvc33tfi4eamyjpb/wish/2618495005 Group 3 https://padlet.com/tclark208/wvc33tfi4eamyjpb/wish/2618497167 When you start with a higher number, it's more likely to find longer series of consecutive non-primes.]]> 2023-06-08 17:10:17 UTC https://padlet.com/tclark208/wvc33tfi4eamyjpb/wish/2618497167 Group 2 mickino https://padlet.com/tclark208/wvc33tfi4eamyjpb/wish/2618498707 Possibly following a similar process to the one proposed by Tim and consider 2x3x4x5x6x7x8.... and eliminate "excessive" factors?]]> 2023-06-08 17:12:41 UTC https://padlet.com/tclark208/wvc33tfi4eamyjpb/wish/2618498707 group x's investigation idea mattcrowe88 https://padlet.com/tclark208/wvc33tfi4eamyjpb/wish/2618499314 we thought about investigating strings of 6 composites from 1-n. We noticed that Tim's simplification of 7! was useful, and possible because 3.4 is 12, which 6 is a factor of. We were heading in the direction of looking at the number of combinations like this involving the numbers 2, 3, 4, 5, 6 and 7, which may take us in the direction we are looking for]]> 2023-06-08 17:13:33 UTC https://padlet.com/tclark208/wvc33tfi4eamyjpb/wish/2618499314