Block #269,813

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 11/23/2013, 11:39:01 AM · Difficulty 9.9522 · 6,533,577 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

f6a9bc2ec0f8b5dbca4264d3e042ae4b4d8350a1e1e61bab19fd2c5c1d27a44c

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Height

#269,813

Difficulty

9.952173

Transactions

Size

1.74 KB

Version

Bits

09f3c19b

Nonce

58,155

Timestamp

11/23/2013, 11:39:01 AM

Confirmations

6,533,577

Mined by

⛏️ aRActSdLxn2ZqjjJWDqtFqLnpPczBTGp8d29

Merkle Root

b30546318976fd9ef418d08a9038bb0740321052757e27424439bf090e3b673d

Transactions (1)

Coinbaseb30546318976fd…39bf090e3b673d

1 in → 48 out10.0600 XPM1.66 KB

ActSdLxn…BTGp8d29 AabHNb1B…GRoingRy AKXeSXzu…yeuNjvhB ANmkKL2U…jPxj1Qs3 ARpndEmc…Hg792kEk

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.

9.503 × 10⁹⁰(91-digit number)

95033387325723853069…84666919890340027999

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

9.503 × 10⁹⁰(91-digit number)

95033387325723853069…84666919890340027999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.900 × 10⁹¹(92-digit number)

19006677465144770613…69333839780680055999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

3.801 × 10⁹¹(92-digit number)

38013354930289541227…38667679561360111999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

7.602 × 10⁹¹(92-digit number)

76026709860579082455…77335359122720223999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.520 × 10⁹²(93-digit number)

15205341972115816491…54670718245440447999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

3.041 × 10⁹²(93-digit number)

30410683944231632982…09341436490880895999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

6.082 × 10⁹²(93-digit number)

60821367888463265964…18682872981761791999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.216 × 10⁹³(94-digit number)

12164273577692653192…37365745963523583999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

2.432 × 10⁹³(94-digit number)

24328547155385306385…74731491927047167999

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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