Block #332,239

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 12/27/2013, 9:45:30 PM · Difficulty 10.1750 · 6,476,386 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

f28a150b669aae5cca73b10d367aa86b65713f1d6bb7df85bf641cf9264d8214

View on Chainz ↗

Height

#332,239

Difficulty

10.174976

Transactions

Size

210 B

Version

Bits

0a2ccb41

Nonce

4,342

Timestamp

12/27/2013, 9:45:30 PM

Confirmations

6,476,386

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

50588bad457fad2430dd6bc02df045f65ee824eb93bc39c4afde28b0897ca681

Transactions (1)

Coinbase50588bad457fad…de28b0897ca681

1 in → 1 out9.6400 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.

1.246 × 10¹⁰³(104-digit number)

12467115996716645738…50974513600790528001

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

1.246 × 10¹⁰³(104-digit number)

12467115996716645738…50974513600790528001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

2.493 × 10¹⁰³(104-digit number)

24934231993433291476…01949027201581056001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

4.986 × 10¹⁰³(104-digit number)

49868463986866582953…03898054403162112001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

9.973 × 10¹⁰³(104-digit number)

99736927973733165906…07796108806324224001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

1.994 × 10¹⁰⁴(105-digit number)

19947385594746633181…15592217612648448001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

3.989 × 10¹⁰⁴(105-digit number)

39894771189493266362…31184435225296896001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

7.978 × 10¹⁰⁴(105-digit number)

79789542378986532725…62368870450593792001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

1.595 × 10¹⁰⁵(106-digit number)

15957908475797306545…24737740901187584001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

3.191 × 10¹⁰⁵(106-digit number)

31915816951594613090…49475481802375168001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

6.383 × 10¹⁰⁵(106-digit number)

63831633903189226180…98950963604750336001

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

Block #332,239

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