Block #486,040

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 4/11/2014, 9:33:52 AM · Difficulty 10.6179 · 6,315,101 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

555548ce50f2312f1b0c6e9505905ceba359fd7175d9fd2024f00bbfc59118bd

View on Chainz ↗

Height

#486,040

Difficulty

10.617945

Transactions

Size

869 B

Version

Bits

0a9e31a7

Nonce

63,984

Timestamp

4/11/2014, 9:33:52 AM

Confirmations

6,315,101

Mined by

⛏️ jaSGAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

f20ea58075f46ada3979e5d69e9c9d74c109962f533d173b3a80f5a3253d4f91

Transactions (1)

Coinbasef20ea58075f46a…80f5a3253d4f91

1 in → 21 out8.8599 XPM777 B

AQvZBsUo…hppgRZTJ ANNg88pG…ppn21sTe AQ8QAT3J…rCFKuVbR AWMrD5hP…ZwsoxvZ3 ATKK7iFz…wZm46KN1

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.

1.218 × 10⁹⁹(100-digit number)

12185079831285365132…61708245883523765761

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

1.218 × 10⁹⁹(100-digit number)

12185079831285365132…61708245883523765761

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

2.437 × 10⁹⁹(100-digit number)

24370159662570730264…23416491767047531521

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

4.874 × 10⁹⁹(100-digit number)

48740319325141460529…46832983534095063041

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

9.748 × 10⁹⁹(100-digit number)

97480638650282921058…93665967068190126081

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

1.949 × 10¹⁰⁰(101-digit number)

19496127730056584211…87331934136380252161

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

3.899 × 10¹⁰⁰(101-digit number)

38992255460113168423…74663868272760504321

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

7.798 × 10¹⁰⁰(101-digit number)

77984510920226336846…49327736545521008641

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

1.559 × 10¹⁰¹(102-digit number)

15596902184045267369…98655473091042017281

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

3.119 × 10¹⁰¹(102-digit number)

31193804368090534738…97310946182084034561

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

6.238 × 10¹⁰¹(102-digit number)

62387608736181069477…94621892364168069121

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