Block #214,749

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 10/17/2013, 4:21:46 PM · Difficulty 9.9240 · 6,581,511 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

cab9f81b9e1d179c6bf57020086fa4cafa2133f4e46b6e09e9807fc644a70d18

View on Chainz ↗

Height

#214,749

Difficulty

9.923993

Transactions

Size

6.09 KB

Version

Bits

09ec8acd

Nonce

1,165,169,300

Timestamp

10/17/2013, 4:21:46 PM

Confirmations

6,581,511

Mined by

⛏️ FR`5nAcS2hSgb9zhiMDDcV5VgFgDMvrTQfHx7Ra

Merkle Root

9772228c2db613c3e98ca9237b16f238796d0f0d0bcc8235c44a41daacdde543

Transactions (1)

Coinbase9772228c2db613…4a41daacdde543

1 in → 179 out10.0631 XPM6.00 KB

AcS2hSgb…TQfHx7Ra AWcD1GpL…2355pP1d AeFbzyLv…uL8iw1RZ AQxL1zky…o52CurGi AKfwt5JY…jsjT5QJQ

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.

1.715 × 10⁹³(94-digit number)

17157096839781483680…65778998038021050959

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

1.715 × 10⁹³(94-digit number)

17157096839781483680…65778998038021050959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

3.431 × 10⁹³(94-digit number)

34314193679562967361…31557996076042101919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

6.862 × 10⁹³(94-digit number)

68628387359125934722…63115992152084203839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.372 × 10⁹⁴(95-digit number)

13725677471825186944…26231984304168407679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

2.745 × 10⁹⁴(95-digit number)

27451354943650373888…52463968608336815359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

5.490 × 10⁹⁴(95-digit number)

54902709887300747777…04927937216673630719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.098 × 10⁹⁵(96-digit number)

10980541977460149555…09855874433347261439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

2.196 × 10⁹⁵(96-digit number)

21961083954920299111…19711748866694522879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

4.392 × 10⁹⁵(96-digit number)

43922167909840598222…39423497733389045759

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

8.784 × 10⁹⁵(96-digit number)

87844335819681196444…78846995466778091519

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