Block #496,956

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 4/17/2014, 8:38:48 AM · Difficulty 10.7611 · 6,302,253 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

2fd2c5a5563e2ce89dd932bdcfa553499fb829d442a3070172653cafd34edc75

View on Chainz ↗

Height

#496,956

Difficulty

10.761144

Transactions

Size

833 B

Version

Bits

0ac2da58

Nonce

206

Timestamp

4/17/2014, 8:38:48 AM

Confirmations

6,302,253

Mined by

⛏️ <aSOAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

940bcea858e301111fb9576dab1d9e97d12ecf0993f99fc1bf9582fe75fa4f5b

Transactions (1)

Coinbase940bcea858e301…9582fe75fa4f5b

1 in → 20 out8.6200 XPM743 B

AQvZBsUo…hppgRZTJ ANNg88pG…ppn21sTe ATKK7iFz…wZm46KN1 AJtNW28X…Syb4Ph5j AHwvxqCN…7z7foF67

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.

1.800 × 10⁹⁵(96-digit number)

18001253137163306753…02446595560932872959

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

1.800 × 10⁹⁵(96-digit number)

18001253137163306753…02446595560932872959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

3.600 × 10⁹⁵(96-digit number)

36002506274326613507…04893191121865745919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

7.200 × 10⁹⁵(96-digit number)

72005012548653227014…09786382243731491839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.440 × 10⁹⁶(97-digit number)

14401002509730645402…19572764487462983679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

2.880 × 10⁹⁶(97-digit number)

28802005019461290805…39145528974925967359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

5.760 × 10⁹⁶(97-digit number)

57604010038922581611…78291057949851934719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.152 × 10⁹⁷(98-digit number)

11520802007784516322…56582115899703869439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

2.304 × 10⁹⁷(98-digit number)

23041604015569032644…13164231799407738879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

4.608 × 10⁹⁷(98-digit number)

46083208031138065289…26328463598815477759

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

9.216 × 10⁹⁷(98-digit number)

92166416062276130578…52656927197630955519

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 First 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 1CC formula:

1CC: p₁ (first prime), p₂ = 2p₁ + 1, p₃ = 2p₂ + 1, …

Cross-reference on Chainz Explorer