prime number power residues and/or indices

John E. Franklin · 2012-01-23 07:51:40

I can walk sideways across a lawn with two hands and two feet, and I usually go to the left, facing toward the ground.

bobbym · 2012-01-23 07:52:35

Did you say you are 235 now? You are very agile for that weight.

John E. Franklin · 2012-01-23 07:57:01

Yeah, I haven't had the submersion test in water to determine how much is fat or muscle though, but I defin(a/i)tely have a ton of muscle and some fat too though. I lifted my 145 pound brother yesterday, and he was as light as a feather. I could easily lift a 200lb person by putting my arms around them if they let me. But the lift by the elbows worked on my brother. Couldn't do it with just biceps, so I bent down and used my legs.

bobbym · 2012-01-23 07:59:27

Ever lift weights? Do any bodybuilding?

John E. Franklin · 2012-01-23 08:03:21

Yup. Everyday just a little for about 6 years now. Every little bit helps, even if it is only five minutes or two minutes, but then repeat it a couple hours later. Gotta go hold my arms out, my favorite exercise, sometimes for eight minutes, yesterday morning eight minutes.

bobbym · 2012-01-23 08:06:30

That is a good idea. Good for the whole system.

John E. Franklin · 2012-01-23 08:17:02

How many minutes do you think I just held my hands out for when I was gone?

bobbym · 2012-01-23 08:20:08

I estimate 8 minutes.

John E. Franklin · 2012-01-23 08:22:10

Yup, exactly 8 minutes and maybe one extra second to make sure on the clock.
After the first 4 minutes when I started with palms facing downward, then I allow a little cheating by turning my palms up, which gives me 3 more minutes, and then for the last minute I switch palms up and down until I can't take the pain anymore which is at 8 minutes and one second today.

bobbym · 2012-01-23 08:23:44

Usually when doing something like that the arms might begin to tremble.

John E. Franklin · 2012-01-23 08:24:32

Yeah mine did for about 4 seconds around the 7th minute but then it stopped.

bobbym · 2012-01-23 08:25:13

That is a long time to be able to do that.

John E. Franklin · 2012-01-23 08:28:40

Thanks. I've been at it for a number of years though. And it helps my handstands I think.

bobbym · 2012-01-23 08:35:35

That will help to increase stamina and resistance to pain.

John E. Franklin · 2012-01-23 08:43:24

I believe whatever you do you get good at, but somethings will overlap to other things and have benefits in other areas. Such as when I went out on the deck and took two split logs (for fireplace)
and moved them in jumping jack style, standing still, flapping arms with logs. Then after coming
back in the house, I feel refreshed and healthier. I just did 44 push-ups from the knees though on the
deck too.

bobbym · 2012-01-23 08:48:14

Whoa! You are becoming a workout nut. Good luck with it, it does make you feel better.

John E. Franklin · 2012-01-23 08:51:28

This is a lazy day compared to most days though really, but thanks for reminding me to exercise with something you said 30 minutes ago.

bobbym · 2012-01-23 08:54:15

What was it?

John E. Franklin · 2012-01-23 09:08:03

Post # 104 got me thinking I hadn't done enough today yet.

bobbym · 2012-01-23 09:23:36

Okay, that is the first time I ever had that effect on anyone. Do not overdo it or you will suffer tomorrow and the day after.

John E. Franklin · 2012-01-23 09:40:11

Believe me when I say this is still lazier than most of my days.
I am a weight and arm-straining addict, remember that arm against arm
hand pushing against hand exercise I mentioned last week, well I usually
do that every day for some time. But if you do it for like an hour with little
breaks, sometimes your heart will tell you stop, that happened once to me.
It was very minor feeling inside I got so I stopped. But I'm not that
hyper lately, that was a couple years ago.

bobbym · 2012-01-23 09:44:10

I know what you mean. You have to know when you have had enough. But usually your body tells you when it is enough.

John E. Franklin · 2012-01-23 09:59:41

Back to power residues though.
Basically for all primes except for the #2, you can
do this stuff in this book. What you do is start with the number one.
Then write the one down. Then double the one and get 2.
Write that down since it is below any odd prime number. Now decide
we are going to do prime #3, the first one in the book. Now
multiply the 2 by 2 and get 4, but modulate (mod) the number 4 down
to 1 with the mod(3) function. 4 = 1 mod(3).
Now you will note you came back to one. So the loop is just 1 and 2, and then 1 and 2.
The ring is of size two, which is one less than the prime number 3.

Now for prime #5, the multiplier of 2 works well too.
Start with 1, though it doesn't matter what number from 1 to 4 you start with because it is
a loop if it works with a multiplier of 2. Just try it to find out if 2 is your multiplier.
1 times 2 is 2. 2 times 2 is 4. The list is 1,2,4 so far. 4 times 2 is 8. 8 mod 5 is 3.
Your list is 1,2,4,3 now. Now 3 times 2 is 6 and 6 mod 5 is 1, you are back to one, the
start of the loop. So the loop size is the prime #5 minus 1 or 4 in length and is 1,2,4,3.

Now the next prime # is 7. For seven, the multiplier of 2 does not work out with a loop of size 6
as desired. Let's see why and then we will try the successful 3 afterwards. Start with 1, double it, 2, double it 4, double it 8. 8 mod 7 is 1, so you have 1,2,4,1,2,4, this is length 3, not 6 as desired.
Now we do it again with the number 3 as the multiplier. Start with 1 triple it 3 triple it 9 mod 7 is 2,
We now have 1,3,2 so far. 2 tripled is 6, 6 tripled is 18, 18 mod 7 is 4, Now we have 1,3,2,6,4.
4 tripled is 12. 12 mod 7 is 5. Now we have 1,3,2,6,4,5. 5 tripled is 15. 15 mod 7 is 1. We are back to the starting value of 1 again and so it would repeat around, so the ring is 1,3,2,6,4,5 for prime # 7. Length is 7-1 or 6.

This is basically how the whole book goes. Also there are indices listed which I can explain later.
The above were the power residues.
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Math Is Fun Forum

#101 2012-01-23 07:51:40

Re: prime number power residues and/or indices

#102 2012-01-23 07:52:35

Re: prime number power residues and/or indices

#103 2012-01-23 07:57:01

Re: prime number power residues and/or indices

#104 2012-01-23 07:59:27

Re: prime number power residues and/or indices

#105 2012-01-23 08:03:21

Re: prime number power residues and/or indices

#106 2012-01-23 08:06:30

Re: prime number power residues and/or indices

#107 2012-01-23 08:17:02

Re: prime number power residues and/or indices

#108 2012-01-23 08:20:08

Re: prime number power residues and/or indices

#109 2012-01-23 08:22:10

Re: prime number power residues and/or indices

#110 2012-01-23 08:23:44

Re: prime number power residues and/or indices

#111 2012-01-23 08:24:32

Re: prime number power residues and/or indices

#112 2012-01-23 08:25:13

Re: prime number power residues and/or indices

#113 2012-01-23 08:28:40

Re: prime number power residues and/or indices

#114 2012-01-23 08:35:35

Re: prime number power residues and/or indices

#115 2012-01-23 08:43:24

Re: prime number power residues and/or indices

#116 2012-01-23 08:48:14

Re: prime number power residues and/or indices

#117 2012-01-23 08:51:28

Re: prime number power residues and/or indices

#118 2012-01-23 08:54:15

Re: prime number power residues and/or indices

#119 2012-01-23 09:08:03

Re: prime number power residues and/or indices

#120 2012-01-23 09:23:36

Re: prime number power residues and/or indices

#121 2012-01-23 09:40:11

Re: prime number power residues and/or indices

#122 2012-01-23 09:44:10

Re: prime number power residues and/or indices

#123 2012-01-23 09:59:41

Re: prime number power residues and/or indices

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