Block #303,902

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 12/10/2013, 3:16:45 PM · Difficulty 9.9932 · 6,495,038 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

81ff5616bdf310d4a1e89091a392f11f39867d444000bf904fa11a23a97a03b1

View on Chainz ↗

Height

#303,902

Difficulty

9.993163

Transactions

Size

1.11 KB

Version

Bits

09fe3ff5

Nonce

18,481

Timestamp

12/10/2013, 3:16:45 PM

Confirmations

6,495,038

Mined by

⛏️ aR1AHuJ9wYhTJUvyVGtJfHi8VJT6eBGmgHrKZ

Merkle Root

0e9e30da92fda620dfa51440c2482a1a46871cb0c3cf7429022b5eca1ecfaf0a

Transactions (1)

Coinbase0e9e30da92fda6…2b5eca1ecfaf0a

1 in → 29 out9.9800 XPM1.02 KB

AHuJ9wYh…BGmgHrKZ AG5YAjec…VhA4Aeh1 AeixXgaM…ikgdEo6Z AN63YyQR…1tfe566A AQwRN8bE…V8PsTcY9

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.

3.911 × 10⁸⁹(90-digit number)

39115593698375810889…66069512252189492641

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

3.911 × 10⁸⁹(90-digit number)

39115593698375810889…66069512252189492641

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

7.823 × 10⁸⁹(90-digit number)

78231187396751621778…32139024504378985281

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

1.564 × 10⁹⁰(91-digit number)

15646237479350324355…64278049008757970561

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

3.129 × 10⁹⁰(91-digit number)

31292474958700648711…28556098017515941121

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

6.258 × 10⁹⁰(91-digit number)

62584949917401297423…57112196035031882241

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

1.251 × 10⁹¹(92-digit number)

12516989983480259484…14224392070063764481

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

2.503 × 10⁹¹(92-digit number)

25033979966960518969…28448784140127528961

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

5.006 × 10⁹¹(92-digit number)

50067959933921037938…56897568280255057921

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

1.001 × 10⁹²(93-digit number)

10013591986784207587…13795136560510115841

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

2.002 × 10⁹²(93-digit number)

20027183973568415175…27590273121020231681

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