Block #326,014

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 12/23/2013, 11:46:43 AM · Difficulty 10.1950 · 6,473,312 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

9c2771263e5405334512ce26e19de2da8e7ae8c12e2be7f2e6adb0ec3b42e70c

View on Chainz ↗

Height

#326,014

Difficulty

10.195040

Transactions

Size

872 B

Version

Bits

0a31ee20

Nonce

71,030

Timestamp

12/23/2013, 11:46:43 AM

Confirmations

6,473,312

Mined by

⛏️ ~aR"Aac9Hjdgnw4T4L2csqLecJsmZjP4ktypc3

Merkle Root

fbd147ac506eb1ae7c1d2ac92b1d33999a6efad571d331f28a5b446511616be9

Transactions (1)

Coinbasefbd147ac506eb1…5b446511616be9

1 in → 21 out9.6100 XPM777 B

Aac9Hjdg…P4ktypc3 AYsbyzmX…rTFNGXyW AG5YAjec…VhA4Aeh1 AamykSCW…5Mjzpr7i APeshfYV…3PKcKMKH

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.

5.008 × 10¹⁰⁶(107-digit number)

50080257013558730813…06350301941530962881

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

5.008 × 10¹⁰⁶(107-digit number)

50080257013558730813…06350301941530962881

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

1.001 × 10¹⁰⁷(108-digit number)

10016051402711746162…12700603883061925761

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

2.003 × 10¹⁰⁷(108-digit number)

20032102805423492325…25401207766123851521

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

4.006 × 10¹⁰⁷(108-digit number)

40064205610846984650…50802415532247703041

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

8.012 × 10¹⁰⁷(108-digit number)

80128411221693969301…01604831064495406081

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

1.602 × 10¹⁰⁸(109-digit number)

16025682244338793860…03209662128990812161

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

3.205 × 10¹⁰⁸(109-digit number)

32051364488677587720…06419324257981624321

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

6.410 × 10¹⁰⁸(109-digit number)

64102728977355175441…12838648515963248641

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

1.282 × 10¹⁰⁹(110-digit number)

12820545795471035088…25677297031926497281

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

2.564 × 10¹⁰⁹(110-digit number)

25641091590942070176…51354594063852994561

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