Block #262,350

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 11/16/2013, 7:11:16 PM · Difficulty 9.9687 · 6,548,793 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

7430913e400795b4e0b393b2fced66e2a015d048d9a676353c4f062a54c2465c

View on Chainz ↗

Height

#262,350

Difficulty

9.968660

Transactions

Size

1.94 KB

Version

Bits

09f7fa14

Nonce

38,407

Timestamp

11/16/2013, 7:11:16 PM

Confirmations

6,548,793

Mined by

⛏️ aRANHbaxZpBSqLnDhrQC2JecyGXbXjnHCJJs

Merkle Root

cd506531c0f735f34570b6a1b68d8f8f79732605a9e0335356d3d5e368041d5e

Transactions (1)

Coinbasecd506531c0f735…d3d5e368041d5e

1 in → 54 out10.0300 XPM1.85 KB

ANHbaxZp…XjnHCJJs AFqKfjez…qX9Ace3g AQtzUSwq…htAuF3yC AMttQDuf…7j6tfS9x 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.

1.570 × 10⁹⁰(91-digit number)

15706193458437569243…33028059946288747201

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

1.570 × 10⁹⁰(91-digit number)

15706193458437569243…33028059946288747201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

3.141 × 10⁹⁰(91-digit number)

31412386916875138486…66056119892577494401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

6.282 × 10⁹⁰(91-digit number)

62824773833750276973…32112239785154988801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.256 × 10⁹¹(92-digit number)

12564954766750055394…64224479570309977601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

2.512 × 10⁹¹(92-digit number)

25129909533500110789…28448959140619955201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

5.025 × 10⁹¹(92-digit number)

50259819067000221578…56897918281239910401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.005 × 10⁹²(93-digit number)

10051963813400044315…13795836562479820801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

2.010 × 10⁹²(93-digit number)

20103927626800088631…27591673124959641601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

4.020 × 10⁹²(93-digit number)

40207855253600177262…55183346249919283201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

8.041 × 10⁹²(93-digit number)

80415710507200354525…10366692499838566401

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

Block #262,350

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