Block #233,802

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 10/29/2013, 10:47:35 PM · Difficulty 9.9431 · 6,570,392 confirmations

1CC

Cunningham Chain of the First Kind

A sequence where each prime is double the previous prime plus one.

Block Header

Block Hash

cd9c3848e7fe7b192ab29e844b242aaf2b552d3c088b0521f700ff459e1fa821

View on Chainz ↗

Height

#233,802

Difficulty

9.943107

Transactions

Size

1.68 KB

Version

Bits

09f16f7c

Nonce

416

Timestamp

10/29/2013, 10:47:35 PM

Confirmations

6,570,392

Mined by

⛏️ JRp:YAZWiC56xr4FNeLHcLNFbmQbZQSNwextJca

Merkle Root

335c4e8b817e4747ec43f0221f2d76992f9c4e392a511109a31910c72452f057

Transactions (1)

Coinbase335c4e8b817e47…1910c72452f057

1 in → 46 out10.0762 XPM1.59 KB

AZWiC56x…NwextJca ASMTaFpz…Dq3jZtyL AdwTEXyC…NwbVbqZV AMypZdXS…5jJKu8wP ANuKx9Ke…wm7nrBRq

Prime Chain Origin

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.

1.397 × 10⁹⁶(97-digit number)

13973752939629601956…29245940869874380799

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

1.397 × 10⁹⁶(97-digit number)

13973752939629601956…29245940869874380799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

2.794 × 10⁹⁶(97-digit number)

27947505879259203912…58491881739748761599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

5.589 × 10⁹⁶(97-digit number)

55895011758518407825…16983763479497523199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.117 × 10⁹⁷(98-digit number)

11179002351703681565…33967526958995046399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

2.235 × 10⁹⁷(98-digit number)

22358004703407363130…67935053917990092799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

4.471 × 10⁹⁷(98-digit number)

44716009406814726260…35870107835980185599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

8.943 × 10⁹⁷(98-digit number)

89432018813629452520…71740215671960371199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.788 × 10⁹⁸(99-digit number)

17886403762725890504…43480431343920742399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

3.577 × 10⁹⁸(99-digit number)

35772807525451781008…86960862687841484799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

7.154 × 10⁹⁸(99-digit number)

71545615050903562016…73921725375682969599

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