Block #203,699

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 10/11/2013, 12:40:28 AM · Difficulty 9.8976 · 6,591,034 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

a3c6f015b01569b6a10f1c4778b672956a045a1678f03673351495a70a3f4443

View on Chainz ↗

Height

#203,699

Difficulty

9.897580

Transactions

Size

718 B

Version

Bits

09e5c7d2

Nonce

38,332

Timestamp

10/11/2013, 12:40:28 AM

Confirmations

6,591,034

Mined by

⛏️ P2SHAWPh3V4bLAUTpZrnMtPLg7AJBJSbWA19so

Merkle Root

c897eb52c04885f52ef41b73dce29378af01d62230ca3eb8207292a4058028b0

Transactions (2)

Coinbase85a1db2c98d311…a808991e42f9ab

1 in → 1 out10.2000 XPM109 B

AWPh3V4b…SbWA19so

4023ed238caf04…e2b56c8adaee21

3 in → 2 out0.5200 XPM520 B

AbomBwim…rhvTvXst AZPzPUf6…EYT2xBu7

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.

1.458 × 10⁹²(93-digit number)

14583569618777118014…55800405125071129841

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

1.458 × 10⁹²(93-digit number)

14583569618777118014…55800405125071129841

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

2.916 × 10⁹²(93-digit number)

29167139237554236028…11600810250142259681

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

5.833 × 10⁹²(93-digit number)

58334278475108472057…23201620500284519361

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.166 × 10⁹³(94-digit number)

11666855695021694411…46403241000569038721

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

2.333 × 10⁹³(94-digit number)

23333711390043388823…92806482001138077441

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

4.666 × 10⁹³(94-digit number)

46667422780086777646…85612964002276154881

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

9.333 × 10⁹³(94-digit number)

93334845560173555292…71225928004552309761

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

1.866 × 10⁹⁴(95-digit number)

18666969112034711058…42451856009104619521

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

3.733 × 10⁹⁴(95-digit number)

37333938224069422117…84903712018209239041

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 Second 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 2CC formula:

2CC: p₁ (first prime), p₂ = 2p₁ − 1, p₃ = 2p₂ − 1, …

Cross-reference on Chainz Explorer