Block #510,471

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 4/25/2014, 4:26:56 PM · Difficulty 10.8251 · 6,284,943 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

456e98da0edaad2e813c57af786a509b923946143daf98d2f10187068763f998

View on Chainz ↗

Height

#510,471

Difficulty

10.825065

Transactions

Size

729 B

Version

Bits

0ad3376e

Nonce

557,251

Timestamp

4/25/2014, 4:26:56 PM

Confirmations

6,284,943

Mined by

⛏️ aSZBATKK7iFzxU98qfet38JZnUDJ7swZm46KN1

Merkle Root

d8fa7411c8294ee931a92aba9c357c6823a7dc3a5871b2ab3b62ec81282f4307

Transactions (1)

Coinbased8fa7411c8294e…62ec81282f4307

1 in → 17 out8.5200 XPM641 B

ATKK7iFz…wZm46KN1 AQvZBsUo…hppgRZTJ ANNg88pG…ppn21sTe AdxPNkWD…ZMa9u34q AUbecsVa…i8zo8qRf

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.

5.511 × 10⁹⁰(91-digit number)

55118724381497418088…70937130757252371739

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

5.511 × 10⁹⁰(91-digit number)

55118724381497418088…70937130757252371739

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.102 × 10⁹¹(92-digit number)

11023744876299483617…41874261514504743479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

2.204 × 10⁹¹(92-digit number)

22047489752598967235…83748523029009486959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

4.409 × 10⁹¹(92-digit number)

44094979505197934470…67497046058018973919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

8.818 × 10⁹¹(92-digit number)

88189959010395868940…34994092116037947839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

1.763 × 10⁹²(93-digit number)

17637991802079173788…69988184232075895679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

3.527 × 10⁹²(93-digit number)

35275983604158347576…39976368464151791359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

7.055 × 10⁹²(93-digit number)

70551967208316695152…79952736928303582719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

1.411 × 10⁹³(94-digit number)

14110393441663339030…59905473856607165439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

2.822 × 10⁹³(94-digit number)

28220786883326678061…19810947713214330879

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