Block #265,814

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 11/19/2013, 10:18:40 PM · Difficulty 9.9616 · 6,525,326 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

60f7de2e695cf5b9c818e03081aaf5665db0f4b134ab37e297ff407363e76a42

View on Chainz ↗

Height

#265,814

Difficulty

9.961580

Transactions

Size

758 B

Version

Bits

09f62a22

Nonce

6,851

Timestamp

11/19/2013, 10:18:40 PM

Confirmations

6,525,326

Merkle Root

9bdd1f3aff685ac7a9ba0375d9e97d7508cf0269816623b8971d418b8eb3245d

Transactions (2)

Coinbasef14abaae9fd7f2…bff1013a2d91f7

1 in → 2 out10.0700 XPM142 B

AKcbk49N…GJbKa7j1 AU6kq4CL…dQBLvxLp

18ef125c469937…097c25841c5868

3 in → 2 out969.6181 XPM522 B

AXaNSksL…uxBAzm4z AbFo28bD…8YNWovWf

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.

7.593 × 10¹⁰³(104-digit number)

75932195444492809412…41821683352102421121

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

7.593 × 10¹⁰³(104-digit number)

75932195444492809412…41821683352102421121

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

1.518 × 10¹⁰⁴(105-digit number)

15186439088898561882…83643366704204842241

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

3.037 × 10¹⁰⁴(105-digit number)

30372878177797123765…67286733408409684481

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

6.074 × 10¹⁰⁴(105-digit number)

60745756355594247530…34573466816819368961

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

1.214 × 10¹⁰⁵(106-digit number)

12149151271118849506…69146933633638737921

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

2.429 × 10¹⁰⁵(106-digit number)

24298302542237699012…38293867267277475841

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

4.859 × 10¹⁰⁵(106-digit number)

48596605084475398024…76587734534554951681

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

9.719 × 10¹⁰⁵(106-digit number)

97193210168950796048…53175469069109903361

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

1.943 × 10¹⁰⁶(107-digit number)

19438642033790159209…06350938138219806721

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

3.887 × 10¹⁰⁶(107-digit number)

38877284067580318419…12701876276439613441

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 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

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 2CC formula:

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

Cross-reference on Chainz Explorer