Block #447,008

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 3/16/2014, 11:11:57 PM · Difficulty 10.3618 · 6,357,785 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

b8d679eb11b8549d9f084a8b2f5be04e7233621eaffdb0da061b2365a151964b

View on Chainz ↗

Height

#447,008

Difficulty

10.361804

Transactions

Size

1.01 KB

Version

Bits

0a5c9f33

Nonce

3,067

Timestamp

3/16/2014, 11:11:57 PM

Confirmations

6,357,785

Mined by

⛏️ aS&AQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

42813eb7c553082f5fb8959df4bf8efa5b57e8cd0775d887a2639c52c7cb18dc

Transactions (1)

Coinbase42813eb7c55308…639c52c7cb18dc

1 in → 26 out9.3000 XPM947 B

AQvZBsUo…hppgRZTJ Aac9Hjdg…P4ktypc3 AGKhfQo2…h7fBXLX6 ALqxX1WA…hsKjbnXn ATKK7iFz…wZm46KN1

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.

1.773 × 10⁹²(93-digit number)

17730168706790703731…83003804862630001301

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

1.773 × 10⁹²(93-digit number)

17730168706790703731…83003804862630001301

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

3.546 × 10⁹²(93-digit number)

35460337413581407462…66007609725260002601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

7.092 × 10⁹²(93-digit number)

70920674827162814925…32015219450520005201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.418 × 10⁹³(94-digit number)

14184134965432562985…64030438901040010401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

2.836 × 10⁹³(94-digit number)

28368269930865125970…28060877802080020801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

5.673 × 10⁹³(94-digit number)

56736539861730251940…56121755604160041601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.134 × 10⁹⁴(95-digit number)

11347307972346050388…12243511208320083201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

2.269 × 10⁹⁴(95-digit number)

22694615944692100776…24487022416640166401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

4.538 × 10⁹⁴(95-digit number)

45389231889384201552…48974044833280332801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

9.077 × 10⁹⁴(95-digit number)

90778463778768403105…97948089666560665601

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