Block #291,201

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 12/3/2013, 1:37:26 AM · Difficulty 9.9897 · 6,512,036 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

701a6174f7dfa0e01012767f0c1b0f3125c5a34b229e4c1d479f6a63a4ea89d3

View on Chainz ↗

Height

#291,201

Difficulty

9.989730

Transactions

Size

1.08 KB

Version

Bits

09fd5ef7

Nonce

21,176

Timestamp

12/3/2013, 1:37:26 AM

Confirmations

6,512,036

Mined by

⛏️ qaR5AZninDSu1Gy3NdWkaTGfLDa2i9FvgDMwC4

Merkle Root

13727063cd3c7395a13a60307b44637711422105b9679d2eb0c300550a489a1d

Transactions (1)

Coinbase13727063cd3c73…c300550a489a1d

1 in → 28 out9.9900 XPM1015 B

AZninDSu…FvgDMwC4 ARzXge7S…CEjL5oYm AHuJ9wYh…BGmgHrKZ Ad9pSzHt…cpJ3y2zz AdyKWr2A…7PSnFqeJ

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.

2.996 × 10⁹⁷(98-digit number)

29969356373998315257…31896114167027558399

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

2.996 × 10⁹⁷(98-digit number)

29969356373998315257…31896114167027558399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

5.993 × 10⁹⁷(98-digit number)

59938712747996630515…63792228334055116799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.198 × 10⁹⁸(99-digit number)

11987742549599326103…27584456668110233599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

2.397 × 10⁹⁸(99-digit number)

23975485099198652206…55168913336220467199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

4.795 × 10⁹⁸(99-digit number)

47950970198397304412…10337826672440934399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

9.590 × 10⁹⁸(99-digit number)

95901940396794608824…20675653344881868799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.918 × 10⁹⁹(100-digit number)

19180388079358921764…41351306689763737599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

3.836 × 10⁹⁹(100-digit number)

38360776158717843529…82702613379527475199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

7.672 × 10⁹⁹(100-digit number)

76721552317435687059…65405226759054950399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

1.534 × 10¹⁰⁰(101-digit number)

15344310463487137411…30810453518109900799

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