Block #466,724

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 3/30/2014, 8:38:18 AM · Difficulty 10.4255 · 6,340,982 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

ce4542ee3dffe02082c6a84665e4d98a97d50639d161048e9fdd9958d6679e2f

View on Chainz ↗

Height

#466,724

Difficulty

10.425475

Transactions

Size

259 B

Version

Bits

0a6cebf2

Nonce

226,817

Timestamp

3/30/2014, 8:38:18 AM

Confirmations

6,340,982

Mined by

AMVf7JrgD9LEuSS2R27DgQAdb3xd5AVR7C

Merkle Root

7812aec01f177444175392f2842c0cb07b737ab059d8972f816246b1e41c7651

Transactions (1)

Coinbase7812aec01f1774…6246b1e41c7651

1 in → 3 out9.1900 XPM165 B

AMVf7Jrg…xd5AVR7C ALzzzbUz…2Cb4jSDN AJno7LX2…vo4wdWtY

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.

1.646 × 10¹⁰³(104-digit number)

16461414044525173230…19611417626285747201

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

1.646 × 10¹⁰³(104-digit number)

16461414044525173230…19611417626285747201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

3.292 × 10¹⁰³(104-digit number)

32922828089050346460…39222835252571494401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

6.584 × 10¹⁰³(104-digit number)

65845656178100692921…78445670505142988801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.316 × 10¹⁰⁴(105-digit number)

13169131235620138584…56891341010285977601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

2.633 × 10¹⁰⁴(105-digit number)

26338262471240277168…13782682020571955201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

5.267 × 10¹⁰⁴(105-digit number)

52676524942480554337…27565364041143910401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.053 × 10¹⁰⁵(106-digit number)

10535304988496110867…55130728082287820801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

2.107 × 10¹⁰⁵(106-digit number)

21070609976992221734…10261456164575641601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

4.214 × 10¹⁰⁵(106-digit number)

42141219953984443469…20522912329151283201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

8.428 × 10¹⁰⁵(106-digit number)

84282439907968886939…41045824658302566401

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 #466,724

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