Block #154,569

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 9/7/2013, 6:23:40 PM · Difficulty 9.8645 · 6,639,572 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

400b9cae908895aeebd26dffbd8b84bf3cd3d954a886dd2850803e04b195633b

View on Chainz ↗

Height

#154,569

Difficulty

9.864527

Transactions

Size

1.64 KB

Version

Bits

09dd519c

Nonce

736,489

Timestamp

9/7/2013, 6:23:40 PM

Confirmations

6,639,572

Merkle Root

67ee6687a91ad3651679a06f032566afa91ff7f642739e83b3023946e1b36532

Transactions (2)

Coinbase207c0f60478d79…cda0a85abffda1

1 in → 1 out10.2800 XPM109 B

AP9mkN5C…Cp9EUL1P

79ae8d08a4698c…89b2a942727812

12 in → 2 out119.3000 XPM1.44 KB

AGZvBxxa…shhkwtTn AGaYbstR…has6cxA4

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.

1.126 × 10⁹²(93-digit number)

11265632267854203221…64143962945540278701

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

1.126 × 10⁹²(93-digit number)

11265632267854203221…64143962945540278701

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

2.253 × 10⁹²(93-digit number)

22531264535708406442…28287925891080557401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

4.506 × 10⁹²(93-digit number)

45062529071416812885…56575851782161114801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

9.012 × 10⁹²(93-digit number)

90125058142833625771…13151703564322229601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

1.802 × 10⁹³(94-digit number)

18025011628566725154…26303407128644459201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

3.605 × 10⁹³(94-digit number)

36050023257133450308…52606814257288918401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

7.210 × 10⁹³(94-digit number)

72100046514266900617…05213628514577836801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

1.442 × 10⁹⁴(95-digit number)

14420009302853380123…10427257029155673601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

2.884 × 10⁹⁴(95-digit number)

28840018605706760246…20854514058311347201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

5.768 × 10⁹⁴(95-digit number)

57680037211413520493…41709028116622694401

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 Second 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 2CC formula:

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

Cross-reference on Chainz Explorer