Superficial, inaccurate research related to Oswald's SS# will be pushed at you..

[Tom Scully]

...if it hasn't been, already. There are enough BS claims advanced, consider refusing to be misled by sensationalists.
The hype seems to be about the fourth and fifth digits of the nine digit SS# assigned to Oswald. ( 433-54-3937 )

https://www.ssa.gov/policy/docs/ssb/v69n2/v69n2p55.html
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.....Group Number
The group number (the fourth and fifth digits of the SSN) was initially determined by the procedure of issuing numbers in groups of 10,000 to post offices for assignment on behalf of the Social Security Board's Bureau of Old-Age Benefits. The group numbers range from 01 to 99 (00 is not used), but for administrative reasons, they are not assigned consecutively. Within each area number allocated to a state, the sequence of group number assignments begins with the odd-numbered group numbers from 01 to 09, followed by even group numbers 10 through 98, then even numbers 02 through 08, and finally odd numbers 11 through 99.4....
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Group Number
The group number (the fourth and fifth digits of the SSN) was initially determined by the procedure of issuing numbers in groups of 10,000 to post offices for assignment on behalf of the Social Security Board's Bureau of Old-Age Benefits. The group numbers range from 01 to 99 (00 is not used), but for administrative reasons, they are not assigned consecutively. Within each area number allocated to a state, the sequence of group number assignments begins with the odd-numbered group numbers from 01 to 09, followed by even group numbers 10 through 98, then even numbers 02 through 08, and finally odd number 11 through 99.(4)

 (4) SSA makes a list of which groups of SSNs have been assigned available at https://www.ssa.gov/employer/ssnvhighgroup.htm .