TITLE: At maximum, only $2$ consecutive dates can be prime.How to prove this wrong?
QUESTION [5 upvotes]: Today is $03-01-2017$(Date written in English notation) and $3012017$ is a prime number. The other prime number dates, when expanded to include the month and the year as I did for $3^{rd}$ Jan $2017$, falling this month are on $11,12,27$ and  $29^{th}$ $\Longrightarrow$ $11012017$, $12012017$,$27012017$ and $29012017$ are prime numbers.
This lead me to a conjecture that in a given year not more than $2$ consecutive dates can be prime. Is there a way I could prove this to be true or false as the case maybe . I dont need a complete proof but some hints that may lead to it.

REPLY [8 votes]: The numbers $$30042119$$ $$1052119$$ and $$2052119$$ correspond to $3$ consecutive "prime-days". 
Even $4$ consecutive "prime-days" are possible, for example
$$29061379$$
$$30061379$$
$$1071379$$
$$2071379$$
$5$ consecutive "prime-days" within a year are impossible because at least one of the numbers must be divisble by $3$