Block #92,195

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 8/1/2013, 12:51:11 PM · Difficulty 9.2047 · 6,700,268 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

975d230fce1df14b527912541cedb58c8ecd7bdc0e56bc1f94f0aef7e3523b11

View on Chainz ↗

Height

#92,195

Difficulty

9.204748

Transactions

Size

726 B

Version

Bits

09346a65

Nonce

12,587

Timestamp

8/1/2013, 12:51:11 PM

Confirmations

6,700,268

Merkle Root

c4bc20ea5cdad09832c7b18d5aadc6b0a40c75ff005bd5e764278151105d8587

Transactions (2)

Coinbase010f22b10d2dd3…06fd47f76ef7cc

1 in → 1 out11.8000 XPM109 B

AXiKff8y…8hN9hz1n

4804a0a7be822c…f2bc9f6d19a99d

3 in → 2 out134.0004 XPM521 B

AUeFimzF…op75Mh53 AS6LA4kY…zo6s6rzE

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.

1.504 × 10¹⁰⁹(110-digit number)

15048280680092475244…90646261303201355359

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

1.504 × 10¹⁰⁹(110-digit number)

15048280680092475244…90646261303201355359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

3.009 × 10¹⁰⁹(110-digit number)

30096561360184950489…81292522606402710719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

6.019 × 10¹⁰⁹(110-digit number)

60193122720369900979…62585045212805421439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.203 × 10¹¹⁰(111-digit number)

12038624544073980195…25170090425610842879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

2.407 × 10¹¹⁰(111-digit number)

24077249088147960391…50340180851221685759

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

4.815 × 10¹¹⁰(111-digit number)

48154498176295920783…00680361702443371519

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

9.630 × 10¹¹⁰(111-digit number)

96308996352591841567…01360723404886743039

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.926 × 10¹¹¹(112-digit number)

19261799270518368313…02721446809773486079

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

3.852 × 10¹¹¹(112-digit number)

38523598541036736627…05442893619546972159

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