Block #252,142

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 11/9/2013, 9:59:40 AM · Difficulty 9.9708 · 6,541,145 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

d2902bac0882cf3d3334decc11d30e63657a9da26fc0861d1ebec20a0b045904

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Height

#252,142

Difficulty

9.970801

Transactions

Size

199 B

Version

Bits

09f8866e

Nonce

12,713

Timestamp

11/9/2013, 9:59:40 AM

Confirmations

6,541,145

Merkle Root

d688f06c72d0beb1ed9a5703f2f70de8bc83827e3c1e6f7c5478ad511e65562e

Transactions (1)

Coinbased688f06c72d0be…78ad511e65562e

1 in → 1 out10.0400 XPM109 B

AbhxmaG6…1cGpBiTv

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.

5.883 × 10⁹⁴(95-digit number)

58832510823941049853…17399364540109788161

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

5.883 × 10⁹⁴(95-digit number)

58832510823941049853…17399364540109788161

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

1.176 × 10⁹⁵(96-digit number)

11766502164788209970…34798729080219576321

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

2.353 × 10⁹⁵(96-digit number)

23533004329576419941…69597458160439152641

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

4.706 × 10⁹⁵(96-digit number)

47066008659152839882…39194916320878305281

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

9.413 × 10⁹⁵(96-digit number)

94132017318305679765…78389832641756610561

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

1.882 × 10⁹⁶(97-digit number)

18826403463661135953…56779665283513221121

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

3.765 × 10⁹⁶(97-digit number)

37652806927322271906…13559330567026442241

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

7.530 × 10⁹⁶(97-digit number)

75305613854644543812…27118661134052884481

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

1.506 × 10⁹⁷(98-digit number)

15061122770928908762…54237322268105768961

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

3.012 × 10⁹⁷(98-digit number)

30122245541857817525…08474644536211537921

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