Block #94,361

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 8/3/2013, 1:19:11 AM · Difficulty 9.2019 · 6,732,775 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

17d559e8069177a5f8ad8b1c7922c5181f596bbb8d974343178b8c2020d7e667

View on Chainz ↗

Height

#94,361

Difficulty

9.201886

Transactions

Size

200 B

Version

Bits

0933aec9

Nonce

1,158,939

Timestamp

8/3/2013, 1:19:11 AM

Confirmations

6,732,775

Mined by

⛏️ P2SHAPgByjJFENDXV16WUG9dXJvNGtqEGzQRkF

Merkle Root

deb27e49d69d390b9466e59e74c7b39f2e4a13b2d35b9e98f14b2d70ffa75308

Transactions (1)

Coinbasedeb27e49d69d39…4b2d70ffa75308

1 in → 1 out11.7900 XPM109 B

APgByjJF…qEGzQRkF

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.

5.946 × 10⁹⁷(98-digit number)

59462692280866495453…34821464296692303119

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

5.946 × 10⁹⁷(98-digit number)

59462692280866495453…34821464296692303119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.189 × 10⁹⁸(99-digit number)

11892538456173299090…69642928593384606239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

2.378 × 10⁹⁸(99-digit number)

23785076912346598181…39285857186769212479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

4.757 × 10⁹⁸(99-digit number)

47570153824693196362…78571714373538424959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

9.514 × 10⁹⁸(99-digit number)

95140307649386392725…57143428747076849919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

1.902 × 10⁹⁹(100-digit number)

19028061529877278545…14286857494153699839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

3.805 × 10⁹⁹(100-digit number)

38056123059754557090…28573714988307399679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

7.611 × 10⁹⁹(100-digit number)

76112246119509114180…57147429976614799359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

1.522 × 10¹⁰⁰(101-digit number)

15222449223901822836…14294859953229598719

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 #94,361

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