Block #948,860

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 2/23/2015, 11:21:15 AM · Difficulty 10.8998 · 5,844,032 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

7c656823066cb733e1ab7da37b61d4448f3231eb5e55b03f9d8eba812b4b4a3e

View on Chainz ↗

Height

#948,860

Difficulty

10.899810

Transactions

Size

728 B

Version

Bits

0ae659f1

Nonce

467,217,229

Timestamp

2/23/2015, 11:21:15 AM

Confirmations

5,844,032

Merkle Root

ccf665423c3d842529c894f673313fca96385bd90831295cddb4d43269428792

Transactions (2)

Coinbase9ddba1827ff417…888c2fcf87d56c

1 in → 1 out8.4200 XPM116 B

ANSXnLY2…Sd25TjkD

e3c22745b22b70…4ed3054243a5cd

3 in → 2 out118.0405 XPM522 B

AJzyns9M…JkGiLb7p AHqAhJKY…jC8vs5ud

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.

1.630 × 10⁹⁵(96-digit number)

16306930198856384831…59193735916632411321

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

1.630 × 10⁹⁵(96-digit number)

16306930198856384831…59193735916632411321

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

3.261 × 10⁹⁵(96-digit number)

32613860397712769663…18387471833264822641

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

6.522 × 10⁹⁵(96-digit number)

65227720795425539327…36774943666529645281

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.304 × 10⁹⁶(97-digit number)

13045544159085107865…73549887333059290561

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

2.609 × 10⁹⁶(97-digit number)

26091088318170215731…47099774666118581121

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

5.218 × 10⁹⁶(97-digit number)

52182176636340431462…94199549332237162241

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.043 × 10⁹⁷(98-digit number)

10436435327268086292…88399098664474324481

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

2.087 × 10⁹⁷(98-digit number)

20872870654536172584…76798197328948648961

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

4.174 × 10⁹⁷(98-digit number)

41745741309072345169…53596394657897297921

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

8.349 × 10⁹⁷(98-digit number)

83491482618144690339…07192789315794595841

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