Big integer arithmetic is vital in cryptography, high-performance computing (HPC), and secure communications, yet traditional ripple-carry multiplication is limited by sequential carry propagation. This study evaluates delayed-carry parallelization for large integer multiplication on a consumer-grade AMD Athlon Silver 3050U CPU using AVX2 instructions and multithreading. Performance was compared against a custom ripple-carry baseline and parallel delayed-carry implementations across operands from 128 to 16,384 bits. Over 50 independent trials, Welch's ANOVA confirmed that the delayed-carry method resulted in statistically significant reductions in execution time (p < .001 for all operand sizes). At 16,384 bits, it reduced the mean computation time from 18.52 µs (ripple-carry) to 7.64 µs (4 threads), achieving a 2.43× speedup. The method demonstrated excellent parallel efficiency, reaching superlinear speedup (>1.0) with two threads. The single-threaded delayed-carry implementation performed comparably to, and at larger operands surpassed, the performance of established libraries like GMP and OpenSSL. The approach demonstrates that delayed-carry parallelization effectively utilizes SIMD-enabled CPUs to accelerate big-integer computations, offering significant potential for cryptographic and HPC applications.