Block #326,240

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 12/23/2013, 3:40:08 PM · Difficulty 10.1942 · 6,468,708 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

747ba73e54ab0d28a90134b6e643db27e0d9a68f1963ad61f088c66300f4d8d0

View on Chainz ↗

Height

#326,240

Difficulty

10.194170

Transactions

Size

1.05 KB

Version

Bits

0a31b525

Nonce

67,100

Timestamp

12/23/2013, 3:40:08 PM

Confirmations

6,468,708

Mined by

⛏️ `aRYAac9Hjdgnw4T4L2csqLecJsmZjP4ktypc3

Merkle Root

8e30268c994d3344a855afae25bc0814fde987a0964ff32c28185c90e90fd69c

Transactions (1)

Coinbase8e30268c994d33…185c90e90fd69c

1 in → 27 out9.6100 XPM981 B

Aac9Hjdg…P4ktypc3 AQ8QAT3J…rCFKuVbR AG5YAjec…VhA4Aeh1 AKwqFUdz…D4jGNKFN AYtDvcGs…VuAcA7m7

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.

4.448 × 10¹⁰¹(102-digit number)

44483198519066164661…94512215900973948801

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

4.448 × 10¹⁰¹(102-digit number)

44483198519066164661…94512215900973948801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

8.896 × 10¹⁰¹(102-digit number)

88966397038132329323…89024431801947897601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

1.779 × 10¹⁰²(103-digit number)

17793279407626465864…78048863603895795201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

3.558 × 10¹⁰²(103-digit number)

35586558815252931729…56097727207791590401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

7.117 × 10¹⁰²(103-digit number)

71173117630505863459…12195454415583180801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

1.423 × 10¹⁰³(104-digit number)

14234623526101172691…24390908831166361601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

2.846 × 10¹⁰³(104-digit number)

28469247052202345383…48781817662332723201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

5.693 × 10¹⁰³(104-digit number)

56938494104404690767…97563635324665446401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

1.138 × 10¹⁰⁴(105-digit number)

11387698820880938153…95127270649330892801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

2.277 × 10¹⁰⁴(105-digit number)

22775397641761876306…90254541298661785601

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