Given a
sequence S of decimals digits, find the smallest prime SP which includes
(embeds) this sequence. Let L(S) = number of digits of S and L(SP) =
number of digits of SP .

For
example :

S = 20
L(S) = 2

SP = 1201 L(SP) = 4

S=
6666666666666 L(S) = 13

SP =166666666666667 L(SP) = 15

S =
987654321987654321987654321987654321 L(S) = 36

SP = 103987654321987654321987654321987654321 L(SP) = 39

The
sequence may begin with '0'

For
example :

S = 00000000000000000000 L(S) = 20

SP = 8000000000000000000009 L(SP) = 22

Now, my questions :

**
1
Find a sequence S for which L(SP) = L(S) + 5**

**
2
Find a sequence S for which L(SP) > L(S) + 5 **

**
3
Given L(S) what is the order of magnitude of L(SP) ?**