Block #337,018

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 12/31/2013, 9:17:07 AM · Difficulty 10.1384 · 6,465,649 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

3c1bde8fbd6dc983a443926e0fb23d592d6502977e0102a6ced24e10c3511b71

View on Chainz ↗

Height

#337,018

Difficulty

10.138358

Transactions

Size

208 B

Version

Bits

0a236b6d

Nonce

607,045

Timestamp

12/31/2013, 9:17:07 AM

Confirmations

6,465,649

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

b8ebd515076da1fb6d7d165e745c9a8690fe5c4fe16674782597641ea5046469

Transactions (1)

Coinbaseb8ebd515076da1…97641ea5046469

1 in → 1 out9.7100 XPM116 B

AbwWkWZt…kawDhufa

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.

3.507 × 10⁹⁹(100-digit number)

35073981610066324926…05405623149422755841

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

3.507 × 10⁹⁹(100-digit number)

35073981610066324926…05405623149422755841

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

7.014 × 10⁹⁹(100-digit number)

70147963220132649853…10811246298845511681

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

1.402 × 10¹⁰⁰(101-digit number)

14029592644026529970…21622492597691023361

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

2.805 × 10¹⁰⁰(101-digit number)

28059185288053059941…43244985195382046721

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

5.611 × 10¹⁰⁰(101-digit number)

56118370576106119883…86489970390764093441

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

1.122 × 10¹⁰¹(102-digit number)

11223674115221223976…72979940781528186881

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

2.244 × 10¹⁰¹(102-digit number)

22447348230442447953…45959881563056373761

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

4.489 × 10¹⁰¹(102-digit number)

44894696460884895906…91919763126112747521

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

8.978 × 10¹⁰¹(102-digit number)

89789392921769791813…83839526252225495041

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

1.795 × 10¹⁰²(103-digit number)

17957878584353958362…67679052504450990081

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