Block #246,241

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 11/5/2013, 11:55:09 PM · Difficulty 9.9643 · 6,564,044 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

8127a74afae759e56fb2dac2fe48279a4b63e7336cff68c72696ab7b660d97d3

View on Chainz ↗

Height

#246,241

Difficulty

9.964334

Transactions

Size

1.61 KB

Version

Bits

09f6de97

Nonce

129,695

Timestamp

11/5/2013, 11:55:09 PM

Confirmations

6,564,044

Mined by

⛏️ Ry4MAPVGazMT74NZfPkrnnhUuKpw9gcDCk2nwA

Merkle Root

07f7316290ecf0be16571be127431f2e337cca109faf22ae78f3f8fc7538481d

Transactions (1)

Coinbase07f7316290ecf0…f3f8fc7538481d

1 in → 44 out10.0400 XPM1.52 KB

APVGazMT…cDCk2nwA ANuKx9Ke…wm7nrBRq AMbCuLHZ…WSoStwkc AcEnwywz…vZtt2xTs 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.

1.602 × 10⁹²(93-digit number)

16024928975176331356…41186018637674840599

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

1.602 × 10⁹²(93-digit number)

16024928975176331356…41186018637674840599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

3.204 × 10⁹²(93-digit number)

32049857950352662712…82372037275349681199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

6.409 × 10⁹²(93-digit number)

64099715900705325424…64744074550699362399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.281 × 10⁹³(94-digit number)

12819943180141065084…29488149101398724799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

2.563 × 10⁹³(94-digit number)

25639886360282130169…58976298202797449599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

5.127 × 10⁹³(94-digit number)

51279772720564260339…17952596405594899199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.025 × 10⁹⁴(95-digit number)

10255954544112852067…35905192811189798399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

2.051 × 10⁹⁴(95-digit number)

20511909088225704135…71810385622379596799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

4.102 × 10⁹⁴(95-digit number)

41023818176451408271…43620771244759193599

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

Block #246,241

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