Block #509,677

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 4/25/2014, 5:11:49 AM · Difficulty 10.8207 · 6,285,170 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

dfed329aa158387ad99891818296ccf19352bbbb34c29854f8007860f9e10c5f

View on Chainz ↗

Height

#509,677

Difficulty

10.820710

Transactions

Size

401 B

Version

Bits

0ad21a11

Nonce

73,665

Timestamp

4/25/2014, 5:11:49 AM

Confirmations

6,285,170

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

7b3f52a640abc57b7221b3dccf8bc7d1195be36a0a6d44dfe7286b4ade5ac49c

Transactions (2)

Coinbasefb59e04350a3e1…cae67f55601615

1 in → 1 out8.5417 XPM116 B

AbwWkWZt…kawDhufa

d5674fa30a28b3…bc79a3e9112400

1 in → 1 out0.9900 XPM192 B

ASYDzXXq…MRQa5KvC

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.

5.890 × 10¹⁰²(103-digit number)

58909520108061791040…59008797198312608349

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

5.890 × 10¹⁰²(103-digit number)

58909520108061791040…59008797198312608349

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.178 × 10¹⁰³(104-digit number)

11781904021612358208…18017594396625216699

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

2.356 × 10¹⁰³(104-digit number)

23563808043224716416…36035188793250433399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

4.712 × 10¹⁰³(104-digit number)

47127616086449432832…72070377586500866799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

9.425 × 10¹⁰³(104-digit number)

94255232172898865665…44140755173001733599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

1.885 × 10¹⁰⁴(105-digit number)

18851046434579773133…88281510346003467199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

3.770 × 10¹⁰⁴(105-digit number)

37702092869159546266…76563020692006934399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

7.540 × 10¹⁰⁴(105-digit number)

75404185738319092532…53126041384013868799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

1.508 × 10¹⁰⁵(106-digit number)

15080837147663818506…06252082768027737599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

3.016 × 10¹⁰⁵(106-digit number)

30161674295327637012…12504165536055475199

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