Block #234,896

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 10/30/2013, 2:34:49 PM · Difficulty 9.9449 · 6,567,828 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

6b36321b2f200858eeef58c774d66a898e7ecd5f42584d5d825a79f07d72b4e2

View on Chainz ↗

Height

#234,896

Difficulty

9.944862

Transactions

Size

2.11 KB

Version

Bits

09f1e27a

Nonce

28,817

Timestamp

10/30/2013, 2:34:49 PM

Confirmations

6,567,828

Mined by

⛏️ RqARn5JoKbCvPXiCsf1vAq1otMGAuGgQuvcP

Merkle Root

d2617152095cb5d109951051241107ebefc0a894eca95451f9e6b94f79f7814f

Transactions (1)

Coinbased2617152095cb5…e6b94f79f7814f

1 in → 59 out10.0700 XPM2.02 KB

ARn5JoKb…uGgQuvcP ANuKx9Ke…wm7nrBRq AXDu24HR…L9o8sC5D AQtzUSwq…htAuF3yC AQZYfdBZ…DVLcLRg8

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.

9.022 × 10⁹²(93-digit number)

90220381677379749780…11732843142764706719

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

9.022 × 10⁹²(93-digit number)

90220381677379749780…11732843142764706719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.804 × 10⁹³(94-digit number)

18044076335475949956…23465686285529413439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

3.608 × 10⁹³(94-digit number)

36088152670951899912…46931372571058826879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

7.217 × 10⁹³(94-digit number)

72176305341903799824…93862745142117653759

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.443 × 10⁹⁴(95-digit number)

14435261068380759964…87725490284235307519

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

2.887 × 10⁹⁴(95-digit number)

28870522136761519929…75450980568470615039

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

5.774 × 10⁹⁴(95-digit number)

57741044273523039859…50901961136941230079

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.154 × 10⁹⁵(96-digit number)

11548208854704607971…01803922273882460159

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

2.309 × 10⁹⁵(96-digit number)

23096417709409215943…03607844547764920319

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

4.619 × 10⁹⁵(96-digit number)

46192835418818431887…07215689095529840639

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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