Block #285,069

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 11/30/2013, 8:55:25 AM · Difficulty 9.9837 · 6,525,250 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

c8ab891f68d0699744b464588c1b92b43b7ed98b2d60fb6622f2f1c54ea40ae8

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Height

#285,069

Difficulty

9.983703

Transactions

Size

1.18 KB

Version

Bits

09fbd3fd

Nonce

17,668

Timestamp

11/30/2013, 8:55:25 AM

Confirmations

6,525,250

Mined by

⛏️ YaRAZ2pPuKgN7GXPJPBLxtm9bkWcE95SN2Yr7

Merkle Root

ba54058e86958693fffc3ec53189ad99d64cc33b7d10add00b0aa97899af76ae

Transactions (1)

Coinbaseba54058e869586…0aa97899af76ae

1 in → 31 out10.0000 XPM1.09 KB

AZ2pPuKg…95SN2Yr7 AGFAJ5YL…ZEnBbk6G AaJwNkvB…uqCwyjYa AWZd1qVJ…9pj9yfPa ANkX1YyE…kHwVW1hd

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.

6.701 × 10⁹⁹(100-digit number)

67012459757556219107…69190830469515644161

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

6.701 × 10⁹⁹(100-digit number)

67012459757556219107…69190830469515644161

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

1.340 × 10¹⁰⁰(101-digit number)

13402491951511243821…38381660939031288321

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

2.680 × 10¹⁰⁰(101-digit number)

26804983903022487643…76763321878062576641

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

5.360 × 10¹⁰⁰(101-digit number)

53609967806044975286…53526643756125153281

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

1.072 × 10¹⁰¹(102-digit number)

10721993561208995057…07053287512250306561

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

2.144 × 10¹⁰¹(102-digit number)

21443987122417990114…14106575024500613121

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

4.288 × 10¹⁰¹(102-digit number)

42887974244835980228…28213150049001226241

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

8.577 × 10¹⁰¹(102-digit number)

85775948489671960457…56426300098002452481

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

1.715 × 10¹⁰²(103-digit number)

17155189697934392091…12852600196004904961

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 Second 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 2CC formula:

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

Cross-reference on Chainz Explorer

Block #285,069

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