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When D is a prime number, no matter the J, no numbers will be skipped
This conjecture came about when I was exploring the Connect the Dots feature on the website NetLogo. I was wondering about what made a number hit or skip dot 1. In my quest to find out, I was playing around with different dot numbers, and both times I choose odd numbers for my dot size, I realized something. I saw that when my dot size is an odd number, no matter the jump size, dot 1 will always be hit, and no numbers will be skipped. But then, I noticed that all of the numbers I did this with were prime numbers, so I tested my theory with the number 15, to see if I can disprove my conjecture, and realized that my original conjecture (When the dot size is an odd number, no matter the jump size, dot 1 will always be hit, and no numbers will be skipped) was wrong:
I then thought “well, this may not work with all odd numbers, but what about all prime numbers?” So I then did my research, and tested out the numbers 13 & 19:
And I saw that my conjecture remained true! From there, I asked a friend to review it, and she tested it out with a D of 11 and found nothing to disprove my conjecture. I thought my final conjecture was going to be When D is a prime number, no matter the J, 1 will always be hit, and no numbers will be skipped. I was ecstatic and set out to write this blog post, but soon realized that something was wrong. What had originally been a research project about what numbers hit dot 1, turned into me wondering what made a D hit all of the dots. This meant that I needed a new conjecture because when no numbers are skipped, 1 is automatically hit, so I changed my conjecture to When D is a prime number, no matter the J, no numbers will be skipped.
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