Share N+/-1 Primality Proofs - Page 11

wblipp · 2013-03-08, 20:21

(20723+1153#)/20723
(29995+1153#)/29995
3^2121*26+1

Code:

(33431+1153#)/33431
(33205+1153#)/33205
(31691+1153#)/31691
(32929+1153#)/32929
(14001+1153#)/14001
(25715+1153#)/25715
(25813+1153#)/25813
(25863+1153#)/25863
(29427+1153#)/29427
(29491+1153#)/29491
(29045+1153#)/29045
(28153+1153#)/28153
(28207+1153#)/28207
(28741+1153#)/28741
(28815+1153#)/28815
(16769+1153#)/16769
(18905+1153#)/18905
(19757+1153#)/19757
(20345+1153#)/20345
(27805+1153#)/27805
(27389+1153#)/27389
(26567+1153#)/26567
(25197+1153#)/25197
(10807+1153#)/10807
(23483+1153#)/23483
(17593+1153#)/17593
(17323+1153#)/17323
(17169+1153#)/17169
(11623+1153#)/11623
(12013+1153#)/12013
(12233+1153#)/12233
(12565+1153#)/12565
(12921+1153#)/12921
(15953+1153#)/15953
(15611+1153#)/15611
(15163+1153#)/15163
(13243+1153#)/13243
(21471+1153#)/21471
(6715+1153#)/6715
(8857+1153#)/8857
(4465+1153#)/4465
(2455+1153#)/2455
(3059+1153#)/3059
(3097+1153#)/3097
(3741+1153#)/3741
(3937+1153#)/3937
(6031+1153#)/6031
(7015+1153#)/7015
(7439+1153#)/7439
(8213+1153#)/8213
(8299+1153#)/8299
(8441+1153#)/8441
(9031+1153#)/9031
(1005+1153#)/1005
(1271+1153#)/1271
(6743+1153#)/6743
(6837+1153#)/6837
(5533+1153#)/5533
(5217+1153#)/5217
(5257+1153#)/5257
(5371+1153#)/5371
(4697+1153#)/4697
(217+1153#)/217
(527+1153#)/527
(611+1153#)/611

A few hours later, still more of this form:
(34465+1153#)/34465
(34505+1153#)/34505
(38141+1153#)/38141
(38683+1153#)/38683
(39697+1153#)/39697

firejuggler · 2013-03-11, 03:54

805!*10+1
proved, by N-1
easy....

firejuggler · 2013-03-20, 21:10

23^4381-22 proven by N-1

wblipp · 2013-03-23, 16:15

10^2292+99 proven by N+1
(9661^577-1)/9660 by N-1

wblipp · 2013-03-26, 02:28

(2^7737*9-1)/17
(10^2342+17)/117
(1263^757-1)/1262
2^7807-31
(2^7814*65-1)/259
21^1786-20
(19^1848*20+1)/21
(7129^617-1)/7128
(2^8012*147+1)/589

wblipp · 2013-04-05, 04:14

10^3546-1001
52^2071-51

wblipp · 2013-04-10, 03:58

(275^881-1)/274
10^2149*5-49
2^7152-513
2^7155+33
(10^2154*26-23)/3

wblipp · 2013-04-12, 15:19

The first one here was especially fun. Somebody had already tried the N-1 proof with inadequate factorization, but had missed the N+1 also had algebraic factors.

(10^2566*2-11)/9
(439^961+1)/(439^31+1)
10^2568*22-31)/9
(830^881-1)/829

ChristianB · 2013-04-12, 16:56

That could have been me, as I tried this out a week ago or so (can't remember the numbers). What's the secret of finding easy ones? All I found needed some real strong sieving in order to factorize. I thought the easy factors are already tested by factordb.

firejuggler · 2013-04-12, 17:46

if you find a prime in the form of
(a^x-1)/(a-1) or a^x-(a-1) or a^x-(a+1) those 3 are easy.

wblipp · 2013-04-13, 00:56

The factordb does a poor job of finding algebraic factors, so I'm mostly spotting cases that have these algebraic factors. I pick a size and list 100 to 1000 PRPs starting at the size from here. Then I scan down the list, looking for numbers with small divisors, such as (10^2566*2-11)/9. The +1 and -1 will have terms that are constant + and - divisor. In this case 11+9 and 11-9. I then do mental arithmetic to see if the result will cancel the factor and or powers. This case was very special because 11+9=2*10 and 11-9=2, so both the sides end up with 10^n-1. If the calculations exceed my rather limited mental math abilities, I move on the the next one.

2013-03-11, 03:54	#112
firejuggler Apr 2010 Over the rainbow 2³·5²·13 Posts	805!10+1 proved, by N-1 easy.... Last fiddled with by firejuggler on 2013-03-11 at 03:54*

2013-03-23, 16:15	#114
wblipp "William" May 2003 New Haven 2366₁₀ Posts	10^2292+99 proven by N+1 (9661^577-1)/9660 by N-1 Last fiddled with by wblipp on 2013-03-23 at 16:23 Reason: add second

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2013-03-20, 21:10	#113
firejuggler Apr 2010 Over the rainbow 101000101000₂ Posts	23^4381-22 proven by N-1

2013-03-26, 02:28	#115
wblipp "William" May 2003 New Haven 2×7×13² Posts	(2^77379-1)/17 (10^2342+17)/117 (1263^757-1)/1262 2^7807-31 (2^781465-1)/259 21^1786-20 (19^184820+1)/21 (7129^617-1)/7128 (2^8012147+1)/589

2013-04-05, 04:14	#116
wblipp "William" May 2003 New Haven 2·7·13² Posts	10^3546-1001 52^2071-51

2013-04-10, 03:58	#117
wblipp "William" May 2003 New Haven 2·7·13² Posts	(275^881-1)/274 10^21495-49 2^7152-513 2^7155+33 (10^215426-23)/3

2013-04-12, 15:19	#118
wblipp "William" May 2003 New Haven 2×7×13² Posts	The first one here was especially fun. Somebody had already tried the N-1 proof with inadequate factorization, but had missed the N+1 also had algebraic factors. (10^25662-11)/9 (439^961+1)/(439^31+1) 10^256822-31)/9 (830^881-1)/829

2013-04-12, 16:56	#119
ChristianB Apr 2013 Germany 100110111₂ Posts	That could have been me, as I tried this out a week ago or so (can't remember the numbers). What's the secret of finding easy ones? All I found needed some real strong sieving in order to factorize. I thought the easy factors are already tested by factordb.

2013-04-12, 17:46	#120
firejuggler Apr 2010 Over the rainbow 2600₁₀ Posts	if you find a prime in the form of (a^x-1)/(a-1) or a^x-(a-1) or a^x-(a+1) those 3 are easy.

2013-04-13, 00:56	#121
wblipp "William" May 2003 New Haven 2×7×13² Posts	The factordb does a poor job of finding algebraic factors, so I'm mostly spotting cases that have these algebraic factors. I pick a size and list 100 to 1000 PRPs starting at the size from here. Then I scan down the list, looking for numbers with small divisors, such as (10^25662-11)/9. The +1 and -1 will have terms that are constant + and - divisor. In this case 11+9 and 11-9. I then do mental arithmetic to see if the result will cancel the factor and or powers. This case was very special because 11+9=210 and 11-9=2, so both the sides end up with 10^n-1. If the calculations exceed my rather limited mental math abilities, I move on the the next one.