Block #690,583

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 8/24/2014, 11:08:08 AM · Difficulty 10.9547 · 6,105,478 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

aac7fa32fdf2346c57e149b4363d4d11ebe748ae2ed42c51e46a7604826b420a

View on Chainz ↗

Height

#690,583

Difficulty

10.954694

Transactions

Size

202 B

Version

Bits

0af466d5

Nonce

188,362

Timestamp

8/24/2014, 11:08:08 AM

Confirmations

6,105,478

Mined by

⛏️ P2SHAYbFBdKztvJRWUEaa1hwf4Ak9pcf926Mct

Merkle Root

c4124ad67dda42f08e6244cdc7cded3c67c6a00e6b4a0e5988fb8ec9d92ad287

Transactions (1)

Coinbasec4124ad67dda42…fb8ec9d92ad287

1 in → 1 out8.3200 XPM109 B

AYbFBdKz…cf926Mct

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.

2.088 × 10¹⁰¹(102-digit number)

20884578678614803473…13519796095816295999

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

2.088 × 10¹⁰¹(102-digit number)

20884578678614803473…13519796095816295999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

4.176 × 10¹⁰¹(102-digit number)

41769157357229606947…27039592191632591999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

8.353 × 10¹⁰¹(102-digit number)

83538314714459213895…54079184383265183999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.670 × 10¹⁰²(103-digit number)

16707662942891842779…08158368766530367999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

3.341 × 10¹⁰²(103-digit number)

33415325885783685558…16316737533060735999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

6.683 × 10¹⁰²(103-digit number)

66830651771567371116…32633475066121471999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.336 × 10¹⁰³(104-digit number)

13366130354313474223…65266950132242943999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

2.673 × 10¹⁰³(104-digit number)

26732260708626948446…30533900264485887999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

5.346 × 10¹⁰³(104-digit number)

53464521417253896893…61067800528971775999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

1.069 × 10¹⁰⁴(105-digit number)

10692904283450779378…22135601057943551999

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