Block #363,386

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 1/17/2014, 9:24:05 AM · Difficulty 10.4133 · 6,435,219 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

e14f905b07a491aef2f6b094175100f2f716673300ee610f8998c5571850cb9a

View on Chainz ↗

Height

#363,386

Difficulty

10.413295

Transactions

Size

869 B

Version

Bits

0a69cdad

Nonce

6,941

Timestamp

1/17/2014, 9:24:05 AM

Confirmations

6,435,219

Mined by

⛏️ zHGAFutDVqJywBDvDDzwUNgUinUiETJTJj6UF

Merkle Root

fab6b2643a38378e64e9b7db6c54a64d4663e8e3a970193181e48422881c60cf

Transactions (1)

Coinbasefab6b2643a3837…e48422881c60cf

1 in → 21 out9.2100 XPM777 B

AFutDVqJ…TJTJj6UF ANVG1nLa…Mo7dugCD Ad6DSiVe…nWiZdsG8 AaJwNkvB…uqCwyjYa AbiuqgvC…zjLCTyEz

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.

4.861 × 10⁹⁹(100-digit number)

48619177201581688142…83975574171529696001

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

4.861 × 10⁹⁹(100-digit number)

48619177201581688142…83975574171529696001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

9.723 × 10⁹⁹(100-digit number)

97238354403163376284…67951148343059392001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

1.944 × 10¹⁰⁰(101-digit number)

19447670880632675256…35902296686118784001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

3.889 × 10¹⁰⁰(101-digit number)

38895341761265350513…71804593372237568001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

7.779 × 10¹⁰⁰(101-digit number)

77790683522530701027…43609186744475136001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

1.555 × 10¹⁰¹(102-digit number)

15558136704506140205…87218373488950272001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

3.111 × 10¹⁰¹(102-digit number)

31116273409012280411…74436746977900544001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

6.223 × 10¹⁰¹(102-digit number)

62232546818024560822…48873493955801088001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

1.244 × 10¹⁰²(103-digit number)

12446509363604912164…97746987911602176001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

2.489 × 10¹⁰²(103-digit number)

24893018727209824328…95493975823204352001

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