Block #263,235

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 11/17/2013, 3:02:30 PM · Difficulty 9.9667 · 6,542,733 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

f834dc36fa264b5de7234d3000ffa6987d8b4cdc428bd74303d5c7a46a0d646a

View on Chainz ↗

Height

#263,235

Difficulty

9.966717

Transactions

Size

423 B

Version

Bits

09f77ac6

Nonce

1,794

Timestamp

11/17/2013, 3:02:30 PM

Confirmations

6,542,733

Mined by

⛏️ P2SHAdGRRh1eP4JFvQMqy7y2pLsryDQmctLb24

Merkle Root

a93695520c3cbe7a17892b298672cb168b9de8f7cd580f32be5fadd159e6ddeb

Transactions (2)

Coinbasea0a22a2b32c47e…702f930f3bf613

1 in → 2 out10.0600 XPM142 B

AdGRRh1e…QmctLb24 Abiw8n3q…ZnZfgvQW

756cff92ad0f58…985cefaf64934d

1 in → 1 out161.6491 XPM191 B

AcUKPiDe…4rznYsnA

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.

5.721 × 10⁹⁴(95-digit number)

57217869789623340781…48914872439109614439

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

5.721 × 10⁹⁴(95-digit number)

57217869789623340781…48914872439109614439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.144 × 10⁹⁵(96-digit number)

11443573957924668156…97829744878219228879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

2.288 × 10⁹⁵(96-digit number)

22887147915849336312…95659489756438457759

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

4.577 × 10⁹⁵(96-digit number)

45774295831698672625…91318979512876915519

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

9.154 × 10⁹⁵(96-digit number)

91548591663397345250…82637959025753831039

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

1.830 × 10⁹⁶(97-digit number)

18309718332679469050…65275918051507662079

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

3.661 × 10⁹⁶(97-digit number)

36619436665358938100…30551836103015324159

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

7.323 × 10⁹⁶(97-digit number)

73238873330717876200…61103672206030648319

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

1.464 × 10⁹⁷(98-digit number)

14647774666143575240…22207344412061296639

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