Block #315,712

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 12/16/2013, 3:55:03 PM · Difficulty 10.1129 · 6,477,342 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

6414442f1fcee4715260ccb6c76fcdeb4775b9820925b2bc64e400ef5a00799b

View on Chainz ↗

Height

#315,712

Difficulty

10.112871

Transactions

Size

1.02 KB

Version

Bits

0a1ce520

Nonce

57,125

Timestamp

12/16/2013, 3:55:03 PM

Confirmations

6,477,342

Merkle Root

3ea3df0959a03380759cb2a52dbedefa7c28eaf4216fc9c83849e774cb49e52f

Transactions (1)

Coinbase3ea3df0959a033…49e774cb49e52f

1 in → 26 out9.7600 XPM947 B

AYtDvcGs…VuAcA7m7 Aac9Hjdg…P4ktypc3 AN3epWvb…BMoYmoee Ab5zCZXa…CLDccFx6 AUW89vJd…BiczGLRw

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.

7.988 × 10¹⁰¹(102-digit number)

79887286920676656025…74240489464802273281

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

7.988 × 10¹⁰¹(102-digit number)

79887286920676656025…74240489464802273281

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

1.597 × 10¹⁰²(103-digit number)

15977457384135331205…48480978929604546561

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

3.195 × 10¹⁰²(103-digit number)

31954914768270662410…96961957859209093121

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

6.390 × 10¹⁰²(103-digit number)

63909829536541324820…93923915718418186241

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

1.278 × 10¹⁰³(104-digit number)

12781965907308264964…87847831436836372481

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

2.556 × 10¹⁰³(104-digit number)

25563931814616529928…75695662873672744961

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

5.112 × 10¹⁰³(104-digit number)

51127863629233059856…51391325747345489921

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

1.022 × 10¹⁰⁴(105-digit number)

10225572725846611971…02782651494690979841

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

2.045 × 10¹⁰⁴(105-digit number)

20451145451693223942…05565302989381959681

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

4.090 × 10¹⁰⁴(105-digit number)

40902290903386447885…11130605978763919361

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