Block #442,404

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 3/13/2014, 7:40:07 PM · Difficulty 10.3495 · 6,353,543 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

bbeb21ff6223b3a17603f9fef9daa9145f56d0b565d384eda5e619ebf112238d

View on Chainz ↗

Height

#442,404

Difficulty

10.349543

Transactions

Size

903 B

Version

Bits

0a597ba9

Nonce

20,272

Timestamp

3/13/2014, 7:40:07 PM

Confirmations

6,353,543

Mined by

AdFLJFhbQJWBJcv1fjoDef6HbwbsaVkAyh

Merkle Root

c79613af6407e578404cb035218331e1c67312872a7ab49c0d65d3afeb34ad57

Transactions (1)

Coinbasec79613af6407e5…65d3afeb34ad57

1 in → 22 out9.3200 XPM811 B

AdFLJFhb…bsaVkAyh ASgUri65…C7NLcyBg AGr6NcPC…PjbbgUJr AdoqUYAy…tJ482T9b AMW1p9oT…2TzdaZxH

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.

7.702 × 10⁹⁹(100-digit number)

77020621108064923901…16542606392833850881

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

7.702 × 10⁹⁹(100-digit number)

77020621108064923901…16542606392833850881

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

1.540 × 10¹⁰⁰(101-digit number)

15404124221612984780…33085212785667701761

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

3.080 × 10¹⁰⁰(101-digit number)

30808248443225969560…66170425571335403521

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

6.161 × 10¹⁰⁰(101-digit number)

61616496886451939121…32340851142670807041

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

1.232 × 10¹⁰¹(102-digit number)

12323299377290387824…64681702285341614081

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

2.464 × 10¹⁰¹(102-digit number)

24646598754580775648…29363404570683228161

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

4.929 × 10¹⁰¹(102-digit number)

49293197509161551296…58726809141366456321

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

9.858 × 10¹⁰¹(102-digit number)

98586395018323102593…17453618282732912641

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

1.971 × 10¹⁰²(103-digit number)

19717279003664620518…34907236565465825281

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

3.943 × 10¹⁰²(103-digit number)

39434558007329241037…69814473130931650561

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