[seqfan] Re: Insert "+" and always get a prime

[Lars Blomberg]

Below are 400 values of S that I have found.
After this, the slope gets very steep and it will require some tricks to get further within reasonable time.
/Lars

11,12,14,16,20,21,23,25,29,30,32,34,38,41,43,47,49,50,52,56,58,61,65,
67,70,74,76,83,85,89,92,94,98,110,112,116,118,130,136,152,158,170,172,
221,227,229,245,265,281,310,316,334,338,356,358,370,376,394,398,425,
443,449,467,485,512,518,536,538,554,556,574,592,598,625,647,661,665,
667,683,710,712,730,736,754,772,776,790,794,821,845,863,881,889,934,
938,952,958,970,974,992,994,998,1112,1130,1198,1310,1316,1598,1756,
1772,1910,1918,1952,1970,1990,2221,2225,2249,2261,2267,2281,2429,2447,
2465,2489,2645,2681,2885,3110,3170,3310,3334,3370,3398,3518,3554,3730,
3736,3794,3934,3974,4229,4247,4265,4267,4427,4445,4463,4643,4825,4883,
5158,5176,5374,5516,5552,5558,5594,5752,5972,5992,6265,6425,6443,6485,
6685,6821,7330,7376,7390,7394,7534,7556,7592,7712,7934,7970,8221,8225,
8821,9118,9172,9190,9338,9370,9374,9512,9598,9710,9734,9752,9910,
11116,11152,11170,11558,11930,13118,13136,13556,15572,15736,15938,
15952,17716,17752,17992,19972,22885,26285,26881,28285,28429,31370,
31756,33118,33538,33554,35116,35776,37190,37556,37790,37930,39158,
39394,42265,44443,44447,46445,48265,51112,53176,53756,53918,55516,
55552,55558,55576,55774,57116,57754,62665,64645,66667,66685,68683,
71536,71572,71716,71752,73156,75374,75556,77152,77554,79330,79370,
82265,82285,82825,82829,84265,86221,88229,88265,88621,91792,93338,
93958,93994,99712,99998,111112,111118,111170,111310,113170,115136,
115198,115772,117116,119792,135158,139138,151156,151592,159118,177556,
193910,199190,222245,226447,226681,282881,282889,311156,319910,331118,
333770,333994,335156,339370,351938,359794,371116,373130,393554,399710,
464447,484445,486685,488489,515116,533176,551558,559952,595592,595598,
626261,644485,684425,686285,711512,719710,753316,755156,773554,777712,
777776,799394,799712,822265,864883,888485,888643,911390,911518,915752,
931130,975772,979592,991118,999994,1115756,1137770,1191518,1197370,
1353136,1379930,1533736,1593538,1711576,1791110,1795912,1915972,
1951958,2442485,2664425,2862445,3155116,3171710,3193198,3195338,
3195398,3315358,3373336,3573716,3737534,3751576,3939118,4468865,
4488245,5115736,5357776,5551376,5579774,5731136,5759594,5959774,
6462667,6824665,6864485,6866683,7113710,7133110,7139390,7153336,
7159172,7311170,7351376,7719370,7959934,7979534,8844449,9171170,
9777910,9959374,11771992,13913170

-----Ursprungligt meddelande-----
Från: SeqFan [mailto:seqfan-bounces at list.seqfan.eu] För Eric Angelini
Skickat: den 22 december 2014 15:49
Till: Sequence Fanatics Discussion list
Ämne: [seqfan] Insert "+" and always get a prime

Hello SeqFans,
Look at those integers:

110,112,116,118,130,136

You will always get a prime if you insert a "+" sign inside them, no matter where:

110 --> 1+10=11 and 11+0=11
112 --> 1+12=13 and 11+2=13
116 --> 17
118 --> 19
130 --> 1+30=31 and 13+0=13
136 --> 1+36=37 and 13+6=19

101 is not an integer with this property as 1+01=2 is not allowed (no substring starting with "0").

I guess S, the sequence of integers that share this property) will start like this:

S = 11, 12, 14, 16, 20, 21, 23, 25, 29, 30, 32, 34, 38, 41, 43, 47, 49, 50, 52, 56, 58, 61, 65, 67, 70, 74, 76, 83, 85, 89, 92, 94, 98, 110, 112, 116, 118, 130, 136,...
Best,
É.









_______________________________________________

Seqfan Mailing list - http://list.seqfan.eu/