Block #353,555

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 1/11/2014, 12:24:39 AM · Difficulty 10.3288 · 6,442,506 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

44d2e50b346c335912ff16aaf87b1febc7845ab5b57c36ecbb74d898328ab16d

View on Chainz ↗

Height

#353,555

Difficulty

10.328804

Transactions

Size

1.02 KB

Version

Bits

0a542c7a

Nonce

447,446

Timestamp

1/11/2014, 12:24:39 AM

Confirmations

6,442,506

Mined by

⛏️ eaRAac9Hjdgnw4T4L2csqLecJsmZjP4ktypc3

Merkle Root

9b855b57de7ddcfece04daee822b4d4c5a5f7e36fbef1efe7f062050c788be67

Transactions (1)

Coinbase9b855b57de7ddc…062050c788be67

1 in → 26 out9.3600 XPM947 B

Aac9Hjdg…P4ktypc3 AYtDvcGs…VuAcA7m7 AQ8QAT3J…rCFKuVbR AUnkFe8H…fvenjA4X AQwRN8bE…V8PsTcY9

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.

4.496 × 10¹⁰²(103-digit number)

44962648911494808282…35879378362105670401

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

4.496 × 10¹⁰²(103-digit number)

44962648911494808282…35879378362105670401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

8.992 × 10¹⁰²(103-digit number)

89925297822989616564…71758756724211340801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

1.798 × 10¹⁰³(104-digit number)

17985059564597923312…43517513448422681601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

3.597 × 10¹⁰³(104-digit number)

35970119129195846625…87035026896845363201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

7.194 × 10¹⁰³(104-digit number)

71940238258391693251…74070053793690726401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

1.438 × 10¹⁰⁴(105-digit number)

14388047651678338650…48140107587381452801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

2.877 × 10¹⁰⁴(105-digit number)

28776095303356677300…96280215174762905601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

5.755 × 10¹⁰⁴(105-digit number)

57552190606713354601…92560430349525811201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

1.151 × 10¹⁰⁵(106-digit number)

11510438121342670920…85120860699051622401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

2.302 × 10¹⁰⁵(106-digit number)

23020876242685341840…70241721398103244801

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