Block #285,537

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 11/30/2013, 12:56:49 PM · Difficulty 9.9844 · 6,541,467 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

a0690ce6cfac8bcd0c25753cc4887092cf343e2decab2711154a8e4d08dd3dbf

View on Chainz ↗

Height

#285,537

Difficulty

9.984388

Transactions

Size

1.08 KB

Version

Bits

09fc00e2

Nonce

79,904

Timestamp

11/30/2013, 12:56:49 PM

Confirmations

6,541,467

Mined by

⛏️ aAPeshfYVKJ2qg4aRhC5FMjPmxg3PKcKMKH

Merkle Root

e13df6a09e5f8c475f9e35e470a8d7cb2cf8cdfd9ea6abb07af914755cf38dcc

Transactions (1)

Coinbasee13df6a09e5f8c…f914755cf38dcc

1 in → 28 out10.0000 XPM1015 B

APeshfYV…3PKcKMKH AWGQhzDN…RDYvugUy AGFAJ5YL…ZEnBbk6G AJ583KJv…3M16nmdw AZ2pPuKg…95SN2Yr7

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.

1.082 × 10⁹³(94-digit number)

10822200760864355865…51705257927309803519

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

1.082 × 10⁹³(94-digit number)

10822200760864355865…51705257927309803519

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

2.164 × 10⁹³(94-digit number)

21644401521728711730…03410515854619607039

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

4.328 × 10⁹³(94-digit number)

43288803043457423460…06821031709239214079

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

8.657 × 10⁹³(94-digit number)

86577606086914846920…13642063418478428159

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.731 × 10⁹⁴(95-digit number)

17315521217382969384…27284126836956856319

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

3.463 × 10⁹⁴(95-digit number)

34631042434765938768…54568253673913712639

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

6.926 × 10⁹⁴(95-digit number)

69262084869531877536…09136507347827425279

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.385 × 10⁹⁵(96-digit number)

13852416973906375507…18273014695654850559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

2.770 × 10⁹⁵(96-digit number)

27704833947812751014…36546029391309701119

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

Block #285,537

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