I am an employee of a US state government which does not participate in Social Security, so neither I nor my employer pay Social Security taxes. (My employer offers a defined-contribution plan instead.)
Prior to this job, I spent a few years working for private employers, in which I did pay Social Security taxes. However, I have fewer than 40 Social Security credits, according to my SSA statement, which I understand is the minimum to be eligible to receive retirement benefits.
Assuming I continue working for my current (state) employer for the rest of my career, I will not earn any more credits. This suggests that, despite having paid some five figures of Social Security taxes (and the same from my previous employers), I will never be eligible to receive any Social Security retirement benefits.
Is this analysis correct, or is there some other way for me to earn some sort of benefit in exchange for the taxes I have paid?