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 No-primes sequence (Posted on 2014-04-07)
Find the smallest 4-digit prime, consisting of odd digits only, such that by inserting another odd digit (new one or not) between each pair of its digits a composite 7-digit number is produced.

Bonus task 1: Find the smallest 7-digit prime (odd digits only), creating a 13-digit composite number .

Bonus task 2: List additional pairs (i.e. prime, digit) that display this feature.

 No Solution Yet Submitted by Ady TZIDON No Rating

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 computer solution Comment 1 of 1

10   P0=1000
20   while Ct<40
30     P0=nxtprm(P0)
40     S=cutspc(str(P0))
41     Good=1
42     for Psn=1 to len(S)
43        if instr("13579",mid(S,Psn,1))=0 then Good=0
44     next
45     if Good then
50     :for D=1 to 9 step 2
55       :S2=""
60       :for Psn=1 to len(S)-1
70           :S2=S2+mid(S,Psn,1)+cutspc(str(D))
100       :next
105       :S2=S2+right(S,1)
110       :if prmdiv(val(S2))<val(S2) then print P0,D:inc Ct
120     :next D
130   wend

finds the first few (including lowest) 4-digit prime and inserted digit:

1117    1
1117    3
1117    5
1117    7
1117    9
1151    1
1151    3
1151    5
1151    7
1153    1
1153    3
1153    5
1153    7
1153    9
1193    1
1193    3
1193    5
1319    1
1373    1
1511    1
1511    3
1511    5
1511    7
1511    9
1531    1
1531    3
1531    5
1531    7
1531    9
1553    1
1553    3
1571    1
1571    3
1579    1
1579    3
1597    1
1597    3
1597    5
1597    7
1597    9

By changing line 10 to

10   P0=1000000

we get the larger primes and composites:

1111151         1
1111151         3
1111151         5
1111151         7
1111151         9
1111157         1
1111157         3
1111157         5
1111157         7
1111157         9
1111333         1
1111333         3
1111333         5
1111333         7
1111333         9
1111339         1
1111339         3
1111339         5
1111339         7
1111339         9
1111351         1
1111351         3
1111351         5
1111351         7
1111351         9
1111379         1
1111379         3
1111379         5
1111379         7
1111379         9
1111393         1
1111393         3
1111393         5
1111393         7
1111393         9
1111399         1
1111399         3
1111399         5
1111399         7
1111399         9

 Posted by Charlie on 2014-04-07 13:46:22

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