The number 274 in the equation
13! + 288^2 = (288*274)^2
appears in Zohar Chadash. In translation:
"At the time of the End of Days, according to the hour of the day, at the time that the sun shines, from the 6th Day, at the time that is ready according to the count of years, of Yovel and Shmitah together, which is רע"ד (Raa'd, 274 in Gematria) from the 6th Day. At that time a single voice is prepared to awaken at the heights of the upper heavens, a sad and bitter voice, such that hasn't been since the day that the world was created."
In the current context, it refers to 274 years from the year 5501, just like 288. The condition of Yovel and Shmitah together appears to point at the end of the year 5775.
At that time a single voice is prepared to awaken at the heights of the upper heavens, a sad and bitter voice, such that hasn't been since the day that the world was created.