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.
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
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Posted by Charlie
on 2014-04-07 13:46:22 |
computer solution
