Is there a conjecture with maximal prime gaps Define $M_n$ to be the $n$th maximal gap between primes. That is, $M_1=1$ thanks to $3-2=1$; $M_2=2$ thanks to $5-3=2$; $M_3=4$ thanks to $11-7=4$; and in general, $M_n = p_{i+1}-p_i$, where $p_i$ is the smallest prime such that $p_{i+1} - p_i > p_{j+1} - p_j$ for all $j < i$.
Is there a conjecture or proof with maximal prime gaps, $M_n$, which says that the gap will not more than double between one maximal to the next, $$\frac{M_{n+1}}{M_n} \le 2$$ for $n>1$, or $$\frac{M_{n+1}}{M_n} < 2$$ for $n>3$?
If yes, who wrote it?
Edit:
Currently, there are three answers, of which only one appears to try to answer the posed question "who wrote it?" or if the conjecture exist. Greg Martin answered with "I haven't seen a conjecture of this type." which seems to point towards this conjecture being an original conjecture. But, there is no one else which agreed with him or changed the statement.
While the extra information of all of the answers is nice, it appears that proving this conjecture would lead to disprove something with the "heuristic analysis using Cramér's model" and how its is used. But I digress, this would be another question. 
I have also not seen a conjecture like this, so I hoped someone else may have and can state a reference that I can source.
Edit 2:
Now four nice answers, but none which answer the question.
 A: I haven't seen a conjecture of this type. It is conjectured that among all primes up to $x$, the largest gap has size like $(\ln x)^2$ or a constant multiple thereof. The next time that gap occurs, each number following the gap will have a roughly $1/\ln x$ probability of being prime (by the prime number theorem). So we expect the next gap to be about $Y\ln x$ larger than the previous one, where $Y$ is a continuous random variable with a Poisson distribution with parameter $\lambda=1$. This implies that the order of magnitude of $M_{N+1}-M_n$ typically has size $\sqrt M_n$ (times a fluctuating constant); in particular, for any $\varepsilon>0$, we should have $M_{n+1}/M_n < 1+\varepsilon$ for sufficiently large $n$.
A: Here's a heuristic analysis using Cramér's model. TL;DR: the conjecture is likely false.
The expected maximal gap in this model is $\log^2n$, so suppose we're looking just after finding just such a gap. The probability that a number is prime is $x=1/\log n$ and so the probability that a given prime will have a gap of length $k+1$ is $x(1-x)^k$. The probability that a given prime will not be followed by a record gap is thus
$$
1-(1-x)^{\log^2n}=1-\left((1-1/\log n)^{\log n}\right)^{\log n}\approx1-e^{-\log n}=1-1/n.
$$
and the probability that a given prime will be followed by a record of at least $k$ times the old one is
$$
(1-x)^{k\log^2n}\approx e^{-k\log n}=n^{-k}.
$$
Combining the two, the probability that the gap will be exceeded by a factor of $k$ or more is
$$
\sum_{i=0}^\infty(1-1/n)^in^{-k}=\frac{n}{n^k}=\frac{1}{n^{k-1}}
$$
and hence $k=2$ is right on the boundary: we expect records to double the previous record infinitely often (since $\int1/n$ diverges), but records should be 2.001 times the previous record finitely often.
Now this is really taking the heuristic too far. Cramér's model is not state of the art, and has been shown to make incorrect predictions on the fine behavior of the primes ([1], [2]). But the basic idea is that there is a phase transition, probably around 2, from ratios that appear infinitely often to finitely often (or never!).
Improvement
A better version would allow the starting gap to be other than $\log^2n$. This crude version is conservative, since a distribution of values would make it easier to get large factors between the two.
In fact, if you redo the calculation supposing that the old record is only $s\log^2 n$ then you expect that gaps of size $1+1/s$ should occur infinitely often. So if you think that a positive proportion of the time the largest prime gap below $n$ is $0.99\log^2n$ then you should get records topping the previous one by a factor of 2+1/99 infinitely often.
Technical Notes
A further improvement would be to take small factors into account (a relative of the so-called W-trick). It's hard to predict the net effect but if anything it would also make larger factors happen more often.
A minor issue is that my analysis uses $1/\log n$ as though it is constant. But the interesting range is the next $n$ primes after $n$, so it suffices to look up to about $n+n\log n$ which has logarithm about $\log n+\log\log n$ which is less than $(1+\varepsilon)\log n$ for any $\varepsilon>0$ and large enough $n$.
Conclusion
The conjecture is on shaky ground. There's good reason to think big ratios of maximal gaps happen infinitely often. On the other hand, looking at the heuristics we're talking about amazingly big numbers before these sorts of events happen. Each event we're looking at is a new maximal prime gap, and a 'success' at any given maximal prime gap has asymptotic probability 0 of happening, getting positive probability only when we integrate over a large number of new maximal prime gaps. But we know only a handful of these, so it's entirely possible that we'll never see only of these megajumps.
Bibliography
[1] János Pintz, Cramér vs. Cramér. On Cramér's probabilistic model for primes, Funct. Approx. Comment. Math. 37 (2007), part 2, pp. 361–376.
[2] H. Maier, Primes in short intervals, Michigan Math. J. 32 (1985), pp. 221–225.
A: This is all some rather shaky heuristics, but here is what I think: 
A random integer n is prime with probability $\frac{1}{\ln{n}}$ and composite with probability $1 - \frac{1}{\ln{n}}$. 
A random integer n is followed by at least $M$ composite numbers with probability $(1 - \frac{1}{\ln{n}})^M$ which is about $\exp (-\frac{M}{\ln{n}})$. That's true for every integer $n$, including integers $n$ which are primes. 
If the record gap so far is $M$, then a prime $p$ is followed by a record gap with probability $\exp (-\frac{M}{\ln{p}})$. It is followed by a gap of length $2M$ or more with probability $\exp (-\frac{2M}{\ln{p}})$. If that prime $p$ is indeed followed by a record gap, then the probability that it is followed by a gap doubling the record is $\exp (-\frac{M}{\ln{p}})$.
So the chance that a prime $p$ is followed by a record gap is the same as the chance that the record gap is twice the previous record gap. The table above shows 75 record gap up to $1.4 * 10^{18}$. The distance between two record gaps is about $8 * 10^{17}$. $\ln p$ is about 40, so the chance for a prime being followed by a record gap is about $\frac{1}{2 * 10^{16}}$. The chance that a record gap is twice the previous gap is also $\frac{1}{2 * 10^{16}}$. So this is very unlikely to happen. 
Anyone who knows how to make $\frac{1}{\ln{p}}$ look nicer? See comment below.
A: This conjecture has a sequence. See OEIS A053695.
This conjecture has also has a solution:
Bounding Maximal gaps with Ramanujan primes
