Block #154,879

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 9/7/2013, 11:25:28 PM · Difficulty 9.8648 · 6,636,939 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

9af4a423b1896ae4fe58b214695c4d51c7a8a0830326177d61fb10e0fcab8724

View on Chainz ↗

Height

#154,879

Difficulty

9.864767

Transactions

Size

424 B

Version

Bits

09dd6163

Nonce

497,429

Timestamp

9/7/2013, 11:25:28 PM

Confirmations

6,636,939

Merkle Root

03542334b9acc1e50b0623ae0c4d1a989927d4ef122199fc53241db9c3097467

Transactions (2)

Coinbasec84d439d8bec96…1099cbf933c22b

1 in → 1 out10.2700 XPM109 B

AJDycDdM…tMKoQrE7

9c38ef252a6ed7…690e79f3c83427

1 in → 2 out3.5989 XPM226 B

AarCrSHo…hQEQtdGo AcN7Mwej…Rnr1man2

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.

1.183 × 10⁹¹(92-digit number)

11836752141894230970…47536025480328189119

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

1.183 × 10⁹¹(92-digit number)

11836752141894230970…47536025480328189119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

2.367 × 10⁹¹(92-digit number)

23673504283788461940…95072050960656378239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

4.734 × 10⁹¹(92-digit number)

47347008567576923880…90144101921312756479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

9.469 × 10⁹¹(92-digit number)

94694017135153847761…80288203842625512959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.893 × 10⁹²(93-digit number)

18938803427030769552…60576407685251025919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

3.787 × 10⁹²(93-digit number)

37877606854061539104…21152815370502051839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

7.575 × 10⁹²(93-digit number)

75755213708123078209…42305630741004103679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.515 × 10⁹³(94-digit number)

15151042741624615641…84611261482008207359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

3.030 × 10⁹³(94-digit number)

30302085483249231283…69222522964016414719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

6.060 × 10⁹³(94-digit number)

60604170966498462567…38445045928032829439

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