First, a list of all Test scores of 300 and above;
David Warner’s 335* was the 31st instance of 300+ in a Test, and the first at Adelaide. Incidentally the previous highest was 299* by DG Bradman vs SA in 1931-32.
It is also the highest in any day-night Test, surpassing Azhar Ali’s 302* at Dubai in 2016-17.
However, it is the second highest score by an Australian player and in Australia, where ML Hayden’s 380 is in first place.
Coming back to the list of 300+ scores above, 27 players have made 31 such scores.
Lara, Gayle, Sehwag and Bradman have 2 such scores each. Bradman and Sehwag came close to getting a third, getting up to 299* and 293 respectively.
It is instructive to see the list of 300+ scores in chronological order.
The first such score was by Andrew Sandham in 1929-30. He remains relatively unknown now:
http://www.espncricinfo.com/england/content/player/20058.html
Prior to this tour of the West Indies, he had played in 10 Tests without a century, He made 152 in the first Test, and rounded this up with 325 and 50 in what was to be his last Test. England made 849 and later set WI over 800 to win. As in the better-known timeless Test at Durban a decade later, the match was called off as England had to catch their ship home.
This record of 325 only lasted for a little over 7 months, as Bradman made 334 at Leeds during the 1930 tour. (His only other triple (304) also came at Leeds in 1934).
Another of Sandham’s records was more durable; his 375 in the match was not surpassed until Greg Chappell made 380 (247* and 133) in 1973-74.
In England’s customary add-on series with New Zealand after the bodyline series of 1932-33, Hammond made 336*. The captain (RES Wyatt) appears to have declared once he crossed Bradman’s record of 334. Even so, there was not enough time to win the Test.
So the record was back with England. Bradman got up to 304 at Leeds in 1934.
At the Oval in 1938, Hutton made sure it remained with England with 364. England’s total of 903/7 dec was the record until the Sri Lankans made 952/6 in 1997.
A famous picture from that Test:
That record of 364 lasted a little less than 20 years, when a relatively unknown all-rounder named Garfield Sobers marked his first Test century with 365*. There was, expectedly, a crowd disturbance when he passed the old mark. But the captain Gerry Alexander declared after this, correctly guessing that there was enough time to bowl out Pakistan twice.
A more detailed account of this innings can be seen here:
https://abn397.wordpress.com/2015/05/05/make-mine-a-double-no-a-triple/
This record stood for just over 36 years, when another West Indian batsman Brian Lara made 375 at St John’s in 1994. An account of this innings:
https://www.espncricinfo.com/story/_/id/21525184/brian-lara-375-world-record-nearly
The West Indies won the series 3-1 with this final Test drawn.
In the second half of the 1990s, there were two determined efforts, with Sri Lanka’s Jayasuriya making 340 in what is still a Test record total of 952/6, and the puzzling score of 334* by Australian captain Mark Taylor who declared at this point. The official story then was that he did not want to go past Bradman’s Australian record. Both these Tests ended in dull draws.
By late 2003, Matthew Hayden got a chance against Zimbabwe. Admittedly its bowling was somewhat better than what it was later, but he did not stop at crossing 375 and made 380 at Perth, still a record for Australia and in Australia. Steve Waugh declared as soon as Hayden was out at 735/6.
Hayden’s record lasted only for 6 months, when Lara reclaimed it again at St. John’s:
As in 1994, this score was not enough for West Indies to win the Test even though England had to follow on. However, England had won the first 3 Tests and thus won the series 3-0. Lara’s 400* was therefore relatively unimportant to the result.
Since then, the closest anyone got was 374 by M Jayawardene in 2006. Warner might well have come close to the record except that rain was forecast for the remainder of the Test. It is yet unclear whether the captain TD Paine attached any special significance to 335 which was Warner’s score when the captain declared. There was enough time to dismiss Pakistan twice with over a day to spare.
abn397 