Block #251,062

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 11/8/2013, 7:52:46 PM · Difficulty 9.9694 · 6,552,990 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

36611e6f7809f553141315cff9ec2aac480f0d36faf61c6cdb49789fbd4c4755

View on Chainz ↗

Height

#251,062

Difficulty

9.969384

Transactions

Size

1.81 KB

Version

Bits

09f8298b

Nonce

22,520

Timestamp

11/8/2013, 7:52:46 PM

Confirmations

6,552,990

Mined by

⛏️ aR}@BARy21RErJbHr8Mrr5vpYP14eN46pBWtQJ2

Merkle Root

99ca61dad82eae46b8f9f7abf7c5f5d82d87d10f4d31f4489adbec479261b156

Transactions (1)

Coinbase99ca61dad82eae…dbec479261b156

1 in → 50 out10.0300 XPM1.72 KB

ARy21REr…6pBWtQJ2 AKXeSXzu…yeuNjvhB ARpndEmc…Hg792kEk AQtzUSwq…htAuF3yC AKDTDDtx…iqvw9cdY

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.

3.825 × 10⁹³(94-digit number)

38255010440071459649…12116134949467033279

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

3.825 × 10⁹³(94-digit number)

38255010440071459649…12116134949467033279

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

7.651 × 10⁹³(94-digit number)

76510020880142919298…24232269898934066559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.530 × 10⁹⁴(95-digit number)

15302004176028583859…48464539797868133119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

3.060 × 10⁹⁴(95-digit number)

30604008352057167719…96929079595736266239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

6.120 × 10⁹⁴(95-digit number)

61208016704114335438…93858159191472532479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

1.224 × 10⁹⁵(96-digit number)

12241603340822867087…87716318382945064959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

2.448 × 10⁹⁵(96-digit number)

24483206681645734175…75432636765890129919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

4.896 × 10⁹⁵(96-digit number)

48966413363291468350…50865273531780259839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

9.793 × 10⁹⁵(96-digit number)

97932826726582936701…01730547063560519679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

1.958 × 10⁹⁶(97-digit number)

19586565345316587340…03461094127121039359

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