Block #447,759

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 3/17/2014, 11:42:08 AM · Difficulty 10.3619 · 6,355,519 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

df9dda9e4f3ee1ecf7366603f9b3d67fd39870e3922eb82a3a6716c38074662c

View on Chainz ↗

Height

#447,759

Difficulty

10.361866

Transactions

Size

970 B

Version

Bits

0a5ca343

Nonce

120,590

Timestamp

3/17/2014, 11:42:08 AM

Confirmations

6,355,519

Mined by

⛏️ aS&AQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

1b3bd33096a8da21551c6e1ab3b7efbb5f46977d87fd54dee2f10b7eaa8e9a26

Transactions (1)

Coinbase1b3bd33096a8da…f10b7eaa8e9a26

1 in → 24 out9.3000 XPM879 B

AQvZBsUo…hppgRZTJ ANNg88pG…ppn21sTe ARpdDdHU…AYvjxpq1 AScAzqGc…BZ6tV1vJ AGKhfQo2…h7fBXLX6

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.

4.213 × 10⁹⁶(97-digit number)

42135401336108052626…73665417051784739501

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

4.213 × 10⁹⁶(97-digit number)

42135401336108052626…73665417051784739501

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

8.427 × 10⁹⁶(97-digit number)

84270802672216105252…47330834103569479001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

1.685 × 10⁹⁷(98-digit number)

16854160534443221050…94661668207138958001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

3.370 × 10⁹⁷(98-digit number)

33708321068886442101…89323336414277916001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

6.741 × 10⁹⁷(98-digit number)

67416642137772884202…78646672828555832001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

1.348 × 10⁹⁸(99-digit number)

13483328427554576840…57293345657111664001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

2.696 × 10⁹⁸(99-digit number)

26966656855109153680…14586691314223328001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

5.393 × 10⁹⁸(99-digit number)

53933313710218307361…29173382628446656001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

1.078 × 10⁹⁹(100-digit number)

10786662742043661472…58346765256893312001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

2.157 × 10⁹⁹(100-digit number)

21573325484087322944…16693530513786624001

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