Block #92,800

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 8/1/2013, 11:07:49 PM · Difficulty 9.2035 · 6,724,384 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

b6ca6ba5f92b14d24c4dd4290c4f43fc5473c5263e0d17ba74ab5c9c8a002919

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Height

#92,800

Difficulty

9.203465

Transactions

Size

206 B

Version

Bits

09341647

Nonce

399,161

Timestamp

8/1/2013, 11:07:49 PM

Confirmations

6,724,384

Mined by

⛏️ P2SHAV6kMea3RBP8MBfwNkoBC8rjz8WSpjvkb2

Merkle Root

ca0260f256e994a814fbe59b81599525b9668ba65be3aea9785cd946111e09b6

Transactions (1)

Coinbaseca0260f256e994…5cd946111e09b6

1 in → 1 out11.7900 XPM109 B

AV6kMea3…WSpjvkb2

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.

1.285 × 10¹¹²(113-digit number)

12855278351053304881…12680609199198679399

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

1.285 × 10¹¹²(113-digit number)

12855278351053304881…12680609199198679399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

2.571 × 10¹¹²(113-digit number)

25710556702106609763…25361218398397358799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

5.142 × 10¹¹²(113-digit number)

51421113404213219527…50722436796794717599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.028 × 10¹¹³(114-digit number)

10284222680842643905…01444873593589435199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

2.056 × 10¹¹³(114-digit number)

20568445361685287811…02889747187178870399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

4.113 × 10¹¹³(114-digit number)

41136890723370575622…05779494374357740799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

8.227 × 10¹¹³(114-digit number)

82273781446741151244…11558988748715481599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.645 × 10¹¹⁴(115-digit number)

16454756289348230248…23117977497430963199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

3.290 × 10¹¹⁴(115-digit number)

32909512578696460497…46235954994861926399

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 #92,800

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