Block #531,577

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 5/8/2014, 2:23:15 PM · Difficulty 10.8945 · 6,295,719 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

84f1e7be6d54e220966d5d10eea08274e8675a57638fea942d310cf8a6b3135f

View on Chainz ↗

Height

#531,577

Difficulty

10.894474

Transactions

Size

800 B

Version

Bits

0ae4fc44

Nonce

96,015

Timestamp

5/8/2014, 2:23:15 PM

Confirmations

6,295,719

Mined by

⛏️ ywAGz9gyZWgxBxAyVrKrWDzMw21kbo8NYQpw

Merkle Root

365859cc87ced2f14123af64d46469a32d2c6c9df669e2e77b718ef16dfe58b9

Transactions (1)

Coinbase365859cc87ced2…718ef16dfe58b9

1 in → 19 out8.4100 XPM709 B

AGz9gyZW…bo8NYQpw AUFKXvnz…342ApNcm ASgUri65…C7NLcyBg AbPcCMg4…719q6mAX AbHY4iza…Yckt2J5W

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.

6.244 × 10⁹⁷(98-digit number)

62449703967773038498…34079694676370337529

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

6.244 × 10⁹⁷(98-digit number)

62449703967773038498…34079694676370337529

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.248 × 10⁹⁸(99-digit number)

12489940793554607699…68159389352740675059

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

2.497 × 10⁹⁸(99-digit number)

24979881587109215399…36318778705481350119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

4.995 × 10⁹⁸(99-digit number)

49959763174218430798…72637557410962700239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

9.991 × 10⁹⁸(99-digit number)

99919526348436861596…45275114821925400479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

1.998 × 10⁹⁹(100-digit number)

19983905269687372319…90550229643850800959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

3.996 × 10⁹⁹(100-digit number)

39967810539374744638…81100459287701601919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

7.993 × 10⁹⁹(100-digit number)

79935621078749489277…62200918575403203839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

1.598 × 10¹⁰⁰(101-digit number)

15987124215749897855…24401837150806407679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

3.197 × 10¹⁰⁰(101-digit number)

31974248431499795711…48803674301612815359

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

Block #531,577

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