Block #437,344

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 3/10/2014, 5:54:07 AM · Difficulty 10.3577 · 6,358,605 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

24249fcaadce4fbaeae2248a07b19ce0c7b24965252f4ae14d28fccbd900089d

View on Chainz ↗

Height

#437,344

Difficulty

10.357706

Transactions

Size

903 B

Version

Bits

0a5b9298

Nonce

264,755

Timestamp

3/10/2014, 5:54:07 AM

Confirmations

6,358,605

Mined by

⛏️ `a6&AdFLJFhbQJWBJcv1fjoDef6HbwbsaVkAyh

Merkle Root

6b2cf9d40b84b929c066b9b50d3be3ec2e27826d9350dcaf61198968307b3000

Transactions (1)

Coinbase6b2cf9d40b84b9…198968307b3000

1 in → 22 out9.3100 XPM811 B

AdFLJFhb…bsaVkAyh AGz9gyZW…bo8NYQpw ASgUri65…C7NLcyBg AUzEPJFG…kYkA5U9V 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.

2.550 × 10⁹⁸(99-digit number)

25504852090784570700…44081474333854386121

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

2.550 × 10⁹⁸(99-digit number)

25504852090784570700…44081474333854386121

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

5.100 × 10⁹⁸(99-digit number)

51009704181569141400…88162948667708772241

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

1.020 × 10⁹⁹(100-digit number)

10201940836313828280…76325897335417544481

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

2.040 × 10⁹⁹(100-digit number)

20403881672627656560…52651794670835088961

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

4.080 × 10⁹⁹(100-digit number)

40807763345255313120…05303589341670177921

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

8.161 × 10⁹⁹(100-digit number)

81615526690510626240…10607178683340355841

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.632 × 10¹⁰⁰(101-digit number)

16323105338102125248…21214357366680711681

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

3.264 × 10¹⁰⁰(101-digit number)

32646210676204250496…42428714733361423361

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

6.529 × 10¹⁰⁰(101-digit number)

65292421352408500992…84857429466722846721

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

1.305 × 10¹⁰¹(102-digit number)

13058484270481700198…69714858933445693441

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