Block #241,267

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 11/3/2013, 2:54:40 AM · Difficulty 9.9577 · 6,575,657 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

ea99e6af735919f6bbb733c537afff2f51b033407b91f8add75bb740f640f79a

View on Chainz ↗

Height

#241,267

Difficulty

9.957676

Transactions

Size

1.21 KB

Version

Bits

09f52a49

Nonce

197,357

Timestamp

11/3/2013, 2:54:40 AM

Confirmations

6,575,657

Mined by

⛏️ sRuAe58nAEbon8TkEL3qBwA5Y17zVGFUA15fv

Merkle Root

c6f437bc1121d105b60ed0ec38e76c8835a1b16390aa2db3ecfd30a0344a9686

Transactions (1)

Coinbasec6f437bc1121d1…fd30a0344a9686

1 in → 32 out10.0500 XPM1.12 KB

Ae58nAEb…GFUA15fv AV4rziFj…QhTLsLyZ AeEcSGAf…HjtsPDKX APVGazMT…cDCk2nwA ANo4YY1x…vnsPRDSU

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.

3.173 × 10⁹²(93-digit number)

31737815689165242003…96402100799634595759

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

3.173 × 10⁹²(93-digit number)

31737815689165242003…96402100799634595759

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

6.347 × 10⁹²(93-digit number)

63475631378330484007…92804201599269191519

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.269 × 10⁹³(94-digit number)

12695126275666096801…85608403198538383039

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

2.539 × 10⁹³(94-digit number)

25390252551332193603…71216806397076766079

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

5.078 × 10⁹³(94-digit number)

50780505102664387206…42433612794153532159

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

1.015 × 10⁹⁴(95-digit number)

10156101020532877441…84867225588307064319

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

2.031 × 10⁹⁴(95-digit number)

20312202041065754882…69734451176614128639

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

4.062 × 10⁹⁴(95-digit number)

40624404082131509764…39468902353228257279

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

8.124 × 10⁹⁴(95-digit number)

81248808164263019529…78937804706456514559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

1.624 × 10⁹⁵(96-digit number)

16249761632852603905…57875609412913029119

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 #241,267

Cookie Preferences