Block #246,406

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 11/6/2013, 2:44:40 AM · Difficulty 9.9643 · 6,563,774 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

61cc5823e853d9bbd860be309f7082f3b0a18b64464275f913ab284db5186fb3

View on Chainz ↗

Height

#246,406

Difficulty

9.964302

Transactions

Size

1.84 KB

Version

Bits

09f6dc85

Nonce

104,184

Timestamp

11/6/2013, 2:44:40 AM

Confirmations

6,563,774

Mined by

⛏️ RyARPbCQVvBa6gwFuRmVLPmHNghRXqcEQjXk

Merkle Root

6303cf4c0975eb86f007e6f51fcdeda8532004b87bd67994a933eba6ed204091

Transactions (1)

Coinbase6303cf4c0975eb…33eba6ed204091

1 in → 51 out10.0400 XPM1.75 KB

ARPbCQVv…XqcEQjXk ARpndEmc…Hg792kEk AMbCuLHZ…WSoStwkc AcEnwywz…vZtt2xTs AHkgKuuD…TkWqWiw1

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.

1.167 × 10⁹⁵(96-digit number)

11673548439733117267…16945387247794857559

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

1.167 × 10⁹⁵(96-digit number)

11673548439733117267…16945387247794857559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

2.334 × 10⁹⁵(96-digit number)

23347096879466234534…33890774495589715119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

4.669 × 10⁹⁵(96-digit number)

46694193758932469068…67781548991179430239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

9.338 × 10⁹⁵(96-digit number)

93388387517864938136…35563097982358860479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.867 × 10⁹⁶(97-digit number)

18677677503572987627…71126195964717720959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

3.735 × 10⁹⁶(97-digit number)

37355355007145975254…42252391929435441919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

7.471 × 10⁹⁶(97-digit number)

74710710014291950508…84504783858870883839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.494 × 10⁹⁷(98-digit number)

14942142002858390101…69009567717741767679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

2.988 × 10⁹⁷(98-digit number)

29884284005716780203…38019135435483535359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

5.976 × 10⁹⁷(98-digit number)

59768568011433560407…76038270870967070719

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

Block #246,406

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