Block #262,806

1CCLength 11★★★☆☆

Cunningham Chain of the First Kind · Discovered 11/17/2013, 5:22:54 AM · Difficulty 9.9677 · 6,536,129 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

63603d878d8f5ed452ab40fea69c2b3ff85a7a2090c00009554a0881ed7f77af

View on Chainz ↗

Height

#262,806

Difficulty

9.967650

Transactions

Size

1.97 KB

Version

Bits

09f7b7ec

Nonce

27,164

Timestamp

11/17/2013, 5:22:54 AM

Confirmations

6,536,129

Mined by

⛏️ aRSAHYKGfAoznQQMb4Fyam7Z3sQ8isXAQr9yG

Merkle Root

fcfd48b31efec60970dc794ba68405d68da592c6f80b6ea8da5f900ad5478a55

Transactions (1)

Coinbasefcfd48b31efec6…5f900ad5478a55

1 in → 55 out10.0300 XPM1.89 KB

AHYKGfAo…sXAQr9yG AFqKfjez…qX9Ace3g AdnG9gQ7…N9B7mA2p AQtzUSwq…htAuF3yC APZy8y6E…QZaGQjfp

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.

5.949 × 10⁸⁹(90-digit number)

59494940263569223059…76696763216356151039

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

5.949 × 10⁸⁹(90-digit number)

59494940263569223059…76696763216356151039

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.189 × 10⁹⁰(91-digit number)

11898988052713844611…53393526432712302079

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

2.379 × 10⁹⁰(91-digit number)

23797976105427689223…06787052865424604159

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

4.759 × 10⁹⁰(91-digit number)

47595952210855378447…13574105730849208319

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

9.519 × 10⁹⁰(91-digit number)

95191904421710756894…27148211461698416639

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

1.903 × 10⁹¹(92-digit number)

19038380884342151378…54296422923396833279

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

3.807 × 10⁹¹(92-digit number)

38076761768684302757…08592845846793666559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

7.615 × 10⁹¹(92-digit number)

76153523537368605515…17185691693587333119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

1.523 × 10⁹²(93-digit number)

15230704707473721103…34371383387174666239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

3.046 × 10⁹²(93-digit number)

30461409414947442206…68742766774349332479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^10 × origin − 1

6.092 × 10⁹²(93-digit number)

60922818829894884412…37485533548698664959

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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