Block #506,088

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 4/22/2014, 8:58:54 PM · Difficulty 10.8127 · 6,294,817 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

ca41407612ccdf8476d69eef9ad538035e1221832d2f1059361275b751c2586c

View on Chainz ↗

Height

#506,088

Difficulty

10.812690

Transactions

Size

434 B

Version

Bits

0ad00c73

Nonce

252,228,278

Timestamp

4/22/2014, 8:58:54 PM

Confirmations

6,294,817

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

5d6bfa7fccf86f4f0d504808d519ac9fcd295d0272a525dd6ade0e4821bef88e

Transactions (2)

Coinbaseca9747747d2118…695a0649889326

1 in → 1 out8.5500 XPM116 B

AbwWkWZt…kawDhufa

e3041e58553f45…4511cd7d6908d6

1 in → 2 out1.9800 XPM227 B

AWf7gRXx…8g2bSnjM AZUkhBGs…C55N1XCH

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.

1.575 × 10⁹⁷(98-digit number)

15754813466983751062…83224445440822011659

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

1.575 × 10⁹⁷(98-digit number)

15754813466983751062…83224445440822011659

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

3.150 × 10⁹⁷(98-digit number)

31509626933967502124…66448890881644023319

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

6.301 × 10⁹⁷(98-digit number)

63019253867935004249…32897781763288046639

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.260 × 10⁹⁸(99-digit number)

12603850773587000849…65795563526576093279

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

2.520 × 10⁹⁸(99-digit number)

25207701547174001699…31591127053152186559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

5.041 × 10⁹⁸(99-digit number)

50415403094348003399…63182254106304373119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.008 × 10⁹⁹(100-digit number)

10083080618869600679…26364508212608746239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

2.016 × 10⁹⁹(100-digit number)

20166161237739201359…52729016425217492479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

4.033 × 10⁹⁹(100-digit number)

40332322475478402719…05458032850434984959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

8.066 × 10⁹⁹(100-digit number)

80664644950956805439…10916065700869969919

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