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Old 2010-12-05, 22:06   #892
lorgix
 
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^I left out the smallest one.

The values of p below 21000 for which both p and p#(p+1)+1 is prime are:

2
5
13
17
19
31
1399
1637
2131
3457
4007
8179
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Old 2010-12-06, 00:37   #893
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Entries accepted.

Last fiddled with by 3.14159 on 2010-12-06 at 00:38
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Old 2010-12-06, 01:15   #894
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Quote:
Originally Posted by lorgix View Post
^I left out the smallest one.

The values of p below 21000 for which both p and p#(p+1)+1 is prime are:

2
5
13
17
19
31

1399
1637
2131
3457
4007
8179
wonder if a pattern connects this with A000043 lol
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Old 2010-12-06, 04:55   #895
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Quote:
Originally Posted by science_man_88 View Post
wonder if a pattern connects this with A000043 lol
Nope, just SLSN -- small primes have, heuristically, a large chance of being in either.
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Old 2010-12-10, 07:08   #896
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Primes:

10080*815!+1 (2025digits)
10080*1105!+1 (2889digits)
10080*1176!+1 (3107digits)
7^709*5^710*3^711*2^712*11+1 (1651digits)
7^979*5^980*3^981*2^982*11+1 (2278digits)
7^1217*5^1218*3^1219*2^1220*11+1 (2830digits)
7^2218*5^2219*3^2220*2^2221*11+1 (5155digits)
7^3041*5^3042*3^3043*2^3044*11+1 (7066digits)

Code:
Primality testing 10080*815!+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 821
Running N-1 test using base 823
Calling Brillhart-Lehmer-Selfridge with factored part 34.32%
10080*815!+1 is prime! (2.2744s+0.0490s)
Primality testing 10080*1105!+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 1117
Calling Brillhart-Lehmer-Selfridge with factored part 36.55%
10080*1105!+1 is prime! (2.6884s+0.0022s)
Primality testing 10080*1176!+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 1187
Running N-1 test using base 1193
Calling Brillhart-Lehmer-Selfridge with factored part 36.19%
10080*1176!+1 is prime! (6.2378s+0.0249s)
Primality testing 7^709*5^710*3^711*2^712*11+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 17
Calling Brillhart-Lehmer-Selfridge with factored part 36.31%
7^709*5^710*3^711*2^712*11+1 is prime! (0.5847s+0.0248s)
Primality testing 7^979*5^980*3^981*2^982*11+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 13
Running N-1 test using base 17
Calling Brillhart-Lehmer-Selfridge with factored part 36.33%
7^979*5^980*3^981*2^982*11+1 is prime! (2.3727s+0.0175s)
Primality testing 7^1217*5^1218*3^1219*2^1220*11+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 17
Calling Brillhart-Lehmer-Selfridge with factored part 36.34%
7^1217*5^1218*3^1219*2^1220*11+1 is prime! (2.0646s+0.0288s)
Primality testing 7^2218*5^2219*3^2220*2^2221*11+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 17
Calling Brillhart-Lehmer-Selfridge with factored part 36.36%
7^2218*5^2219*3^2220*2^2221*11+1 is prime! (6.7099s+0.0245s)
Primality testing 7^3041*5^3042*3^3043*2^3044*11+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 17
Calling Brillhart-Lehmer-Selfridge with factored part 36.37%
7^3041*5^3042*3^3043*2^3044*11+1 is prime! (13.1968s+0.0218s)
PRPs

(7^1476*5^1477*3^1478*2^1479*11+1)/31
(10080*2992!+1)/11503
(7^2869*5^2870*3^2871*2^2872*11+1)/75917
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Old 2010-12-10, 07:34   #897
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15120*2568!+10080*2569!+1 (7651digits)


Code:
Primality testing 15120*2568!+10080*2569!+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 2617
Running N-1 test using base 2621
Running N-1 test using base 2657
Running N-1 test using base 2663
Running N-1 test using base 2671
Calling Brillhart-Lehmer-Selfridge with factored part 35.25%
15120*2568!+10080*2569!+1 is prime! (105.9886s+0.0402s)
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Old 2010-12-10, 11:15   #898
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Entries accepted.

I have some of my own to make;

71271*2^26560+1 (8000 digits)

Verification:

Primality testing 71271*2^26560+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Special modular reduction using all-complex FFT length 2048 on 71271*2^26560+1
Calling Brillhart-Lehmer-Selfridge with factored part 99.94%
71271*2^26560+1 is prime! (0.7443s+0.0008s)

Last fiddled with by 3.14159 on 2010-12-10 at 11:17
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Old 2010-12-10, 23:40   #899
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11030*(1459!*p(1459)#)+1 (9217 digits)

Primality testing 11030*(1459!*p(1459)#)+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 12211
Generic modular reduction using generic reduction FFT length 3072 on A 30618-bit number
Running N-1 test using base 12227
Generic modular reduction using generic reduction FFT length 3072 on A 30618-bit number
Calling Brillhart-Lehmer-Selfridge with factored part 33.47%
11030*(1459!*p(1459)#)+1 is prime! (12.1666s+0.0025s)
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Old 2010-12-11, 17:14   #900
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2^9140*1876^1876+1 (8892 digits)

Verification:

Primality testing 2^9140*1876^1876+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Generic modular reduction using generic reduction FFT length 3072 on A 29541-bit number
Calling Brillhart-Lehmer-Selfridge with factored part 43.65%
2^9140*1876^1876+1 is prime! (3.8436s+0.0338s)

Last fiddled with by 3.14159 on 2010-12-11 at 17:14
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Old 2010-12-12, 17:41   #901
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Quote:
Originally Posted by kar_bon View Post
This is more important!

I have to check, if I can find a prime with a factor > 2^30!

Sorry, this had to be written here!
To revive something really, really old:

Code:
99377920784457684856550960479745940901
64666131211740072258387715944910566019
65199332814723985788488412425571863189
134227265351845434830226643974295759
20114396830690557791854295131458080669
48488294828064170392636118382825527761
29733362907781795100360604969781019101
9912045034665551062954595703799022537
27890821152554614466716726879492117627
56149385059814271114560482293446816851
93622219257275277672227712023598606547
3487420014897480879427220128043207311
64482363283807816942169815293627649721
59861915385526732604363198307628291241
55019526435347105896307887044201585643
4223046868698402388548958678158501563
29383379898743107456154686619748794699
48913202047069884870792148206384299807
82548298748190376571022219496340660243
33727149864077643327999914370388402981
58107848701852108340545777352728911041
44999520026254077709863385604821050983
97373124518136695183139324940483157927
78717702373531150598841061135215916703
60165085553395955635247614432753343761
38839102761585561245630366139080123653
12080974559459142496798452654712747321
75114583311012384364772620352306195317
13814292335568012637476080822724008687
99992321558638729860196097361276268037
49852978151176014565978877560996439909
88502760658190877688304553070014357023
30692595349114505346182056415805289037
83815681905286356459078740887488794281
22087476205579164507101645254956012457
64422958281457622052696657152272522601
71581774525997367075767789873071416823
47194456604384032867094490847828351829
89988257609759646068627076141940941791
84720383582230912689350907187204543757
22161763905378578086150480729408606697
40427339607248350669101483847366046423
69254285630932560320954386732752120047
70536525692152931286653161563854300179
34748380044066109705060335906624048553
40965623226509218354786469304891425567
49888567448116579078737320781551547449
23266219973405625117019822154776040767
59498803217030489050226296119311837563
79091267337333036013503753082391257139
42662011976159076591575211734706698333
34442907438990161640620815937463346157
18352578451912834705283601586147292297
95613301979437675921091107986894461821
All have factors > 2^30. And are primes.

Last fiddled with by 3.14159 on 2010-12-12 at 17:41
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Old 2010-12-12, 19:46   #902
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I'll submit 1073741827, as expected.
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