Block #361,109

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 1/15/2014, 8:43:40 PM · Difficulty 10.4037 · 6,444,948 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

89555311d07de21f3b8adbaccdac9f04a436be0a4da99244903b77cba22bd766

View on Chainz ↗

Height

#361,109

Difficulty

10.403697

Transactions

Size

1.05 KB

Version

Bits

0a6758aa

Nonce

77,001

Timestamp

1/15/2014, 8:43:40 PM

Confirmations

6,444,948

Mined by

⛏️ aRAZV4TwxQjib54Zzk9TCxNRouXM8JnQqSoH

Merkle Root

ae555e64534e7e9f4e91d5611337762e4eb143ce2fbc44dbd1b0fbea0a7b203b

Transactions (1)

Coinbaseae555e64534e7e…b0fbea0a7b203b

1 in → 27 out9.2200 XPM981 B

AZV4TwxQ…8JnQqSoH Aac9Hjdg…P4ktypc3 AL8CJrXc…ReWqhicJ AP5UvYhU…vLTDwkdA AQwRN8bE…V8PsTcY9

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.

9.692 × 10⁹⁸(99-digit number)

96929819223480004104…59572422242908693761

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

9.692 × 10⁹⁸(99-digit number)

96929819223480004104…59572422242908693761

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

1.938 × 10⁹⁹(100-digit number)

19385963844696000820…19144844485817387521

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

3.877 × 10⁹⁹(100-digit number)

38771927689392001641…38289688971634775041

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

7.754 × 10⁹⁹(100-digit number)

77543855378784003283…76579377943269550081

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

1.550 × 10¹⁰⁰(101-digit number)

15508771075756800656…53158755886539100161

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

3.101 × 10¹⁰⁰(101-digit number)

31017542151513601313…06317511773078200321

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

6.203 × 10¹⁰⁰(101-digit number)

62035084303027202627…12635023546156400641

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

1.240 × 10¹⁰¹(102-digit number)

12407016860605440525…25270047092312801281

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

2.481 × 10¹⁰¹(102-digit number)

24814033721210881050…50540094184625602561

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

4.962 × 10¹⁰¹(102-digit number)

49628067442421762101…01080188369251205121

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