Limit of Difference between Consecutive Prime Numbers/Historical Note

Historical Note on Limit of Difference between Consecutive Prime Numbers
showed that $E \le \dfrac {15} {16}$.

and showed in $1966$ that $E \le \dfrac {2 + \sqrt 3} 8 \approx 0 \cdotp 46650 \ldots$

In their $1983$ work, and  report that  deduced in $1972$ that $E \le \dfrac {2 \sqrt 2 - 1} 4 \approx 0 \cdotp 45706 \ldots$

However, it is not clear who is or was, and this has not been corroborated.

In $1973$ showed that $E \le \dfrac 1 4 + \dfrac \pi {16} \approx 0 \cdotp 44634 \, 95408 \ldots$