Block #419,613

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 2/25/2014, 7:01:11 PM · Difficulty 10.3744 · 6,375,261 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

00c1c364826fdb4dff274cce6c5abdde92be218fa87f849e022e0b7d686d560e

View on Chainz ↗

Height

#419,613

Difficulty

10.374388

Transactions

Size

840 B

Version

Bits

0a5fd7df

Nonce

107,500

Timestamp

2/25/2014, 7:01:11 PM

Confirmations

6,375,261

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

cc7bfa13eefc724b06d6c5bd1ba6871c4e64a3300ea8ab6e609469ccd5da6874

Transactions (2)

Coinbaseaa19d94c571adf…1f01d6b1e2da85

1 in → 1 out9.2900 XPM110 B

AeKNrjNj…1NEq95Ta

4061e2b8449b30…b33715efcb6d9f

4 in → 1 out997.9900 XPM635 B

AURk8ANT…AMaWTnKo

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.

1.342 × 10¹⁰⁶(107-digit number)

13421763744344714351…76768848637898920961

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

1.342 × 10¹⁰⁶(107-digit number)

13421763744344714351…76768848637898920961

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

2.684 × 10¹⁰⁶(107-digit number)

26843527488689428703…53537697275797841921

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

5.368 × 10¹⁰⁶(107-digit number)

53687054977378857406…07075394551595683841

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.073 × 10¹⁰⁷(108-digit number)

10737410995475771481…14150789103191367681

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

2.147 × 10¹⁰⁷(108-digit number)

21474821990951542962…28301578206382735361

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

4.294 × 10¹⁰⁷(108-digit number)

42949643981903085925…56603156412765470721

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

8.589 × 10¹⁰⁷(108-digit number)

85899287963806171850…13206312825530941441

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

1.717 × 10¹⁰⁸(109-digit number)

17179857592761234370…26412625651061882881

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

3.435 × 10¹⁰⁸(109-digit number)

34359715185522468740…52825251302123765761

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

6.871 × 10¹⁰⁸(109-digit number)

68719430371044937480…05650502604247531521

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