Block #431,492

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) — it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

7.366 × 10⁹⁷(98-digit number)

73667790678844302863…26428293967805687039

Discovered Prime Numbers

p_k = 2^k × origin − 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

origin − 1

7.366 × 10⁹⁷(98-digit number)

73667790678844302863…26428293967805687039

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.473 × 10⁹⁸(99-digit number)

14733558135768860572…52856587935611374079

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

2.946 × 10⁹⁸(99-digit number)

29467116271537721145…05713175871222748159

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

5.893 × 10⁹⁸(99-digit number)

58934232543075442290…11426351742445496319

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.178 × 10⁹⁹(100-digit number)

11786846508615088458…22852703484890992639

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

2.357 × 10⁹⁹(100-digit number)

23573693017230176916…45705406969781985279

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

4.714 × 10⁹⁹(100-digit number)

47147386034460353832…91410813939563970559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

9.429 × 10⁹⁹(100-digit number)

94294772068920707664…82821627879127941119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

1.885 × 10¹⁰⁰(101-digit number)

18858954413784141532…65643255758255882239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

3.771 × 10¹⁰⁰(101-digit number)

37717908827568283065…31286511516511764479

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 10 consecutive prime numbers forming a Cunningham Chain of the First Kind. The prime chain origin — the large number shown above — anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

★★☆☆☆

Rarity

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)

Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — those factors are the primorial divisor. The chain then extends from the first prime using the 1CC formula:

1CC: p₁ (first prime), p₂ = 2p₁ + 1, p₃ = 2p₂ + 1, …

Cross-reference on Chainz Explorer

Block #431,492

Cookie Preferences