Block #317,353

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 12/17/2013, 3:13:30 PM · Difficulty 10.1551 · 6,481,824 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

f1dc0c4958594c83cdaf8ffa9275c9ff3027263be1d48914d126ade296db4c88

View on Chainz ↗

Height

#317,353

Difficulty

10.155091

Transactions

Size

1.08 KB

Version

Bits

0a27b407

Nonce

10,464

Timestamp

12/17/2013, 3:13:30 PM

Confirmations

6,481,824

Mined by

⛏️ aRj*Aac9Hjdgnw4T4L2csqLecJsmZjP4ktypc3

Merkle Root

ab9a6d95074c58dad81efd53a2baecf8279713817fbac2f1cd746a69118b6c1e

Transactions (1)

Coinbaseab9a6d95074c58…746a69118b6c1e

1 in → 28 out9.6600 XPM1014 B

Aac9Hjdg…P4ktypc3 Ad9pSzHt…cpJ3y2zz AYtDvcGs…VuAcA7m7 AebWhrRm…K61Qrkws AcC2zSod…rtWatH79

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.

5.498 × 10¹⁰¹(102-digit number)

54983245084695994208…04423820510630735361

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

5.498 × 10¹⁰¹(102-digit number)

54983245084695994208…04423820510630735361

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

1.099 × 10¹⁰²(103-digit number)

10996649016939198841…08847641021261470721

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

2.199 × 10¹⁰²(103-digit number)

21993298033878397683…17695282042522941441

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

4.398 × 10¹⁰²(103-digit number)

43986596067756795366…35390564085045882881

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

8.797 × 10¹⁰²(103-digit number)

87973192135513590733…70781128170091765761

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

1.759 × 10¹⁰³(104-digit number)

17594638427102718146…41562256340183531521

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

3.518 × 10¹⁰³(104-digit number)

35189276854205436293…83124512680367063041

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

7.037 × 10¹⁰³(104-digit number)

70378553708410872586…66249025360734126081

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

1.407 × 10¹⁰⁴(105-digit number)

14075710741682174517…32498050721468252161

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

2.815 × 10¹⁰⁴(105-digit number)

28151421483364349034…64996101442936504321

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