Block #387,842

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 2/3/2014, 9:53:17 AM · Difficulty 10.4154 · 6,415,207 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

b7504e5ac67afb294b8b391c43535897e092e9738af33c1067937f57156fe6e8

View on Chainz ↗

Height

#387,842

Difficulty

10.415441

Transactions

Size

576 B

Version

Bits

0a6a5a58

Nonce

59,942

Timestamp

2/3/2014, 9:53:17 AM

Confirmations

6,415,207

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

49bdad8e02527eb4f55c287854eb26bad9ffc31a41a59a22059bd04c187efcd9

Transactions (2)

Coinbase297f36a0cdb641…446d645585f685

1 in → 1 out9.2100 XPM110 B

AeKNrjNj…1NEq95Ta

b843e8b0f7d4e0…c6c5b1d800ca5a

2 in → 2 out3.0107 XPM375 B

AXC5EVbv…uoRCscBa AYKNXPrs…MPPeqWKr

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.

1.786 × 10⁹⁷(98-digit number)

17864488149027496434…72904762525494190079

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

1.786 × 10⁹⁷(98-digit number)

17864488149027496434…72904762525494190079

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

3.572 × 10⁹⁷(98-digit number)

35728976298054992869…45809525050988380159

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

7.145 × 10⁹⁷(98-digit number)

71457952596109985739…91619050101976760319

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.429 × 10⁹⁸(99-digit number)

14291590519221997147…83238100203953520639

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

2.858 × 10⁹⁸(99-digit number)

28583181038443994295…66476200407907041279

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

5.716 × 10⁹⁸(99-digit number)

57166362076887988591…32952400815814082559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.143 × 10⁹⁹(100-digit number)

11433272415377597718…65904801631628165119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

2.286 × 10⁹⁹(100-digit number)

22866544830755195436…31809603263256330239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

4.573 × 10⁹⁹(100-digit number)

45733089661510390873…63619206526512660479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

9.146 × 10⁹⁹(100-digit number)

91466179323020781746…27238413053025320959

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 First 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 1CC formula:

1CC: p₁ (first prime), p₂ = 2p₁ + 1, p₃ = 2p₂ + 1, …

Cross-reference on Chainz Explorer