Block #266,836

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 11/20/2013, 6:26:25 PM · Difficulty 9.9602 · 6,524,168 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

eaabede93eff67f1c195b2dd1d4e2fdcc5ea8c2abac9b6057141ce613f2a6970

View on Chainz ↗

Height

#266,836

Difficulty

9.960172

Transactions

Size

676 B

Version

Bits

09f5cdd5

Nonce

157,322

Timestamp

11/20/2013, 6:26:25 PM

Confirmations

6,524,168

Merkle Root

2025eb3adf0bf3014b4bf235342ceacb6ed299eb9346b313b5148f40c914f6c1

Transactions (2)

Coinbase4ed8e1544a5da3…3eb87442401862

1 in → 1 out10.0800 XPM110 B

AeKNrjNj…1NEq95Ta

a9d1d30527c8bf…0716c7d397e240

2 in → 7 out20.1000 XPM477 B

AeKNrjNj…1NEq95Ta Ac52HjfZ…tL3Rs7Sd AbJ2m1AL…BeT5jPVi ALpGM3cL…qWV82qmz AJRvjyJe…EYtxohPp

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.

1.090 × 10⁹³(94-digit number)

10907358773533957396…98003543772484509649

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

1.090 × 10⁹³(94-digit number)

10907358773533957396…98003543772484509649

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

2.181 × 10⁹³(94-digit number)

21814717547067914793…96007087544969019299

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

4.362 × 10⁹³(94-digit number)

43629435094135829586…92014175089938038599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

8.725 × 10⁹³(94-digit number)

87258870188271659172…84028350179876077199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.745 × 10⁹⁴(95-digit number)

17451774037654331834…68056700359752154399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

3.490 × 10⁹⁴(95-digit number)

34903548075308663668…36113400719504308799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

6.980 × 10⁹⁴(95-digit number)

69807096150617327337…72226801439008617599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.396 × 10⁹⁵(96-digit number)

13961419230123465467…44453602878017235199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

2.792 × 10⁹⁵(96-digit number)

27922838460246930935…88907205756034470399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

5.584 × 10⁹⁵(96-digit number)

55845676920493861870…77814411512068940799

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