Block #387,188

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 2/2/2014, 10:42:36 PM · Difficulty 10.4161 · 6,430,676 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

0373e75a5fc063811ee8fe8ad3fe34921f0cb95b637e7e269195c4c2b83ee4c8

View on Chainz ↗

Height

#387,188

Difficulty

10.416088

Transactions

Size

830 B

Version

Bits

0a6a84bb

Nonce

229,872

Timestamp

2/2/2014, 10:42:36 PM

Confirmations

6,430,676

Mined by

⛏️ taRAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

2b95d0b9f7714489ff85b74fa79f18cbe17189b2a05c0dbaea13c9cf11da0602

Transactions (1)

Coinbase2b95d0b9f77144…13c9cf11da0602

1 in → 20 out9.2000 XPM743 B

AQvZBsUo…hppgRZTJ Aac9Hjdg…P4ktypc3 AGKhfQo2…h7fBXLX6 AZV4TwxQ…8JnQqSoH AdDH1inU…KWPvb5kJ

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.

3.876 × 10⁸⁸(89-digit number)

38765087119898890584…35108505931159487759

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

3.876 × 10⁸⁸(89-digit number)

38765087119898890584…35108505931159487759

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

7.753 × 10⁸⁸(89-digit number)

77530174239797781169…70217011862318975519

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.550 × 10⁸⁹(90-digit number)

15506034847959556233…40434023724637951039

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

3.101 × 10⁸⁹(90-digit number)

31012069695919112467…80868047449275902079

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

6.202 × 10⁸⁹(90-digit number)

62024139391838224935…61736094898551804159

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

1.240 × 10⁹⁰(91-digit number)

12404827878367644987…23472189797103608319

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

2.480 × 10⁹⁰(91-digit number)

24809655756735289974…46944379594207216639

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

4.961 × 10⁹⁰(91-digit number)

49619311513470579948…93888759188414433279

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

9.923 × 10⁹⁰(91-digit number)

99238623026941159897…87777518376828866559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

1.984 × 10⁹¹(92-digit number)

19847724605388231979…75555036753657733119

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

Block #387,188

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