Block #254,288

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 11/10/2013, 3:15:52 PM · Difficulty 9.9730 · 6,548,352 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

fc311504761c794ebb5b7538e5eaf8b601a10732765403d549141b7eb9c31e38

View on Chainz ↗

Height

#254,288

Difficulty

9.973047

Transactions

Size

1.84 KB

Version

Bits

09f919a0

Nonce

337,312

Timestamp

11/10/2013, 3:15:52 PM

Confirmations

6,548,352

Mined by

⛏️ PaRAQtzUSwqWuHwFQkN36sUayCVJshtAuF3yC

Merkle Root

a46090d5487bfc833b0221692aa96cfe22920de701ac4d0d3123a9d4048ad2ce

Transactions (1)

Coinbasea46090d5487bfc…23a9d4048ad2ce

1 in → 51 out10.0200 XPM1.75 KB

AQtzUSwq…htAuF3yC AcRG9vnh…TuQSD8LP AKDTDDtx…iqvw9cdY AJzWx2VD…j4ZSMit5 ARjgNH4d…BU7Drh7C

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.

1.061 × 10⁹⁸(99-digit number)

10616286107058402376…48651078221586609999

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

1.061 × 10⁹⁸(99-digit number)

10616286107058402376…48651078221586609999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

2.123 × 10⁹⁸(99-digit number)

21232572214116804752…97302156443173219999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

4.246 × 10⁹⁸(99-digit number)

42465144428233609505…94604312886346439999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

8.493 × 10⁹⁸(99-digit number)

84930288856467219010…89208625772692879999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.698 × 10⁹⁹(100-digit number)

16986057771293443802…78417251545385759999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

3.397 × 10⁹⁹(100-digit number)

33972115542586887604…56834503090771519999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

6.794 × 10⁹⁹(100-digit number)

67944231085173775208…13669006181543039999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.358 × 10¹⁰⁰(101-digit number)

13588846217034755041…27338012363086079999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

2.717 × 10¹⁰⁰(101-digit number)

27177692434069510083…54676024726172159999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

5.435 × 10¹⁰⁰(101-digit number)

54355384868139020166…09352049452344319999

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