Block #384,941

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 2/1/2014, 11:11:37 AM · Difficulty 10.4027 · 6,423,197 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

7793b21fc199e86369494d577f394096910b79cc3b3222f39f9aa5b390bcc168

View on Chainz ↗

Height

#384,941

Difficulty

10.402695

Transactions

Size

763 B

Version

Bits

0a671701

Nonce

57,865

Timestamp

2/1/2014, 11:11:37 AM

Confirmations

6,423,197

Mined by

⛏️ aRAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

759409fd4130545680514aa09e551dbadef884174839fb40fb01195dd6dbab73

Transactions (1)

Coinbase759409fd413054…01195dd6dbab73

1 in → 18 out9.2300 XPM675 B

AQvZBsUo…hppgRZTJ Aac9Hjdg…P4ktypc3 AGKhfQo2…h7fBXLX6 AZV4TwxQ…8JnQqSoH 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.

2.874 × 10⁹⁰(91-digit number)

28748106864068359538…13160623773288906559

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

2.874 × 10⁹⁰(91-digit number)

28748106864068359538…13160623773288906559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

5.749 × 10⁹⁰(91-digit number)

57496213728136719076…26321247546577813119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.149 × 10⁹¹(92-digit number)

11499242745627343815…52642495093155626239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

2.299 × 10⁹¹(92-digit number)

22998485491254687630…05284990186311252479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

4.599 × 10⁹¹(92-digit number)

45996970982509375260…10569980372622504959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

9.199 × 10⁹¹(92-digit number)

91993941965018750521…21139960745245009919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.839 × 10⁹²(93-digit number)

18398788393003750104…42279921490490019839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

3.679 × 10⁹²(93-digit number)

36797576786007500208…84559842980980039679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

7.359 × 10⁹²(93-digit number)

73595153572015000417…69119685961960079359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

1.471 × 10⁹³(94-digit number)

14719030714403000083…38239371923920158719

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 #384,941

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