Block #261,025

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 11/15/2013, 3:48:55 AM · Difficulty 9.9745 · 6,539,612 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

57ea0d9cc5ffa91e91bc3507d7e8b878acff206c0b8782316776910820492df9

View on Chainz ↗

Height

#261,025

Difficulty

9.974473

Transactions

Size

1.77 KB

Version

Bits

09f97716

Nonce

1,019,342

Timestamp

11/15/2013, 3:48:55 AM

Confirmations

6,539,612

Mined by

⛏️ aRAdddtBJ9B8jgQk9Y1MoEheJWPKertkfUpX

Merkle Root

f7505bcb2c3e8087702d49aed04f0f62838d994a776b4ff8512d4a14b6f9dfac

Transactions (1)

Coinbasef7505bcb2c3e80…2d4a14b6f9dfac

1 in → 49 out10.0197 XPM1.69 KB

AdddtBJ9…ertkfUpX AQtzUSwq…htAuF3yC ANHbaxZp…XjnHCJJs ALSiuDiS…WqQxGQSY ATaiAP5C…o4tqgUvu

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.

2.339 × 10⁹¹(92-digit number)

23394149461179587706…16405398151041921161

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

2.339 × 10⁹¹(92-digit number)

23394149461179587706…16405398151041921161

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

4.678 × 10⁹¹(92-digit number)

46788298922359175412…32810796302083842321

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

9.357 × 10⁹¹(92-digit number)

93576597844718350825…65621592604167684641

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.871 × 10⁹²(93-digit number)

18715319568943670165…31243185208335369281

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

3.743 × 10⁹²(93-digit number)

37430639137887340330…62486370416670738561

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

7.486 × 10⁹²(93-digit number)

74861278275774680660…24972740833341477121

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.497 × 10⁹³(94-digit number)

14972255655154936132…49945481666682954241

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

2.994 × 10⁹³(94-digit number)

29944511310309872264…99890963333365908481

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

5.988 × 10⁹³(94-digit number)

59889022620619744528…99781926666731816961

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

1.197 × 10⁹⁴(95-digit number)

11977804524123948905…99563853333463633921

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