Block #262,652

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 11/17/2013, 1:08:08 AM · Difficulty 9.9683 · 6,533,663 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

f581b31060714b4ef728275da24b2d10d90969901e3df2f6d6a625740fa9bc71

View on Chainz ↗

Height

#262,652

Difficulty

9.968320

Transactions

Size

1.58 KB

Version

Bits

09f7e3d2

Nonce

22,593

Timestamp

11/17/2013, 1:08:08 AM

Confirmations

6,533,663

Mined by

⛏️ aRAJ83QDaoSnQQgeKxvuLGszzGf7DqWdAVWo

Merkle Root

742287e107c32451c4026ed9d2fae31785da0da5149b1e5b162045b8ba6806d1

Transactions (1)

Coinbase742287e107c324…2045b8ba6806d1

1 in → 43 out10.0300 XPM1.49 KB

AJ83QDao…DqWdAVWo AHUMdCV5…eXnCsijo AQtzUSwq…htAuF3yC APZy8y6E…QZaGQjfp AN4KokSc…8oFYPA8o

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.

3.690 × 10⁹⁵(96-digit number)

36907589140085490308…43880345744010604759

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

3.690 × 10⁹⁵(96-digit number)

36907589140085490308…43880345744010604759

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

7.381 × 10⁹⁵(96-digit number)

73815178280170980616…87760691488021209519

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.476 × 10⁹⁶(97-digit number)

14763035656034196123…75521382976042419039

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

2.952 × 10⁹⁶(97-digit number)

29526071312068392246…51042765952084838079

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

5.905 × 10⁹⁶(97-digit number)

59052142624136784493…02085531904169676159

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

1.181 × 10⁹⁷(98-digit number)

11810428524827356898…04171063808339352319

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

2.362 × 10⁹⁷(98-digit number)

23620857049654713797…08342127616678704639

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

4.724 × 10⁹⁷(98-digit number)

47241714099309427594…16684255233357409279

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

9.448 × 10⁹⁷(98-digit number)

94483428198618855189…33368510466714818559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

1.889 × 10⁹⁸(99-digit number)

18896685639723771037…66737020933429637119

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