{"generator":"numbers.prime","version":1,"value":[{"decimal":"12222490357377234577","hex":"0xa99f0238f61b7691","bits":64,"safe":false,"twin":false},{"decimal":"14674304780503810349","hex":"0xcba59a7337bf012d","bits":64,"safe":false,"twin":false},{"decimal":"14239910421454161601","hex":"0xc59e5315002886c1","bits":64,"safe":false,"twin":false},{"decimal":"10060720179229274903","hex":"0x8b9edbb2f390b317","bits":64,"safe":false,"twin":false},{"decimal":"9731081920689750347","hex":"0x870bbf730af0414b","bits":64,"safe":false,"twin":false}],"display":"12222490357377234577\n14674304780503810349\n14239910421454161601\n10060720179229274903\n9731081920689750347","meta":{"bits":64,"found":5,"candidates_tested":121,"rejected_by_trial_division":94,"expected_candidates_per_prime":22.2,"rounds":40,"false_positive_bound":"4^-40, about 1 in 10^24 \u2014 far below the odds of the hardware getting the arithmetic wrong","exhausted":false,"search_budget":643,"width_capped":null,"sensitive":true,"note":"Probable primes, not proven ones: forty Miller\u2013Rabin rounds with witnesses drawn from the same seeded stream as the candidates. There is no permalink, for the same reason there is none on the password generator \u2014 a prime anyone can regenerate from a link is not key material.","stream_bytes_used":4520,"rejections":0,"entropy_in_bytes":16,"duration_us":20306},"receipt":{"source":"nist-beacon","source_label":"NIST Randomness Beacon","class":"B","class_label":"Public beacon","caveat":"Published openly \u2014 anyone can look this value up after the fact.","narrative":"NIST Beacon pulse #1,941,357 \u2014 chained to every pulse before it, and signed.","proof_url":"https:\/\/beacon.nist.gov\/beacon\/2.0\/chain\/2\/pulse\/1941357","reference":"1941357","observed_at":"2026-09-14T18:03:00+00:00","degraded":false,"mixed_with_csprng":true,"latency_ms":126,"cached":false},"uses_entropy":true,"reproducible":true}