Block #113,196

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 8/12/2013, 9:46:56 AM · Difficulty 9.7305 · 6,713,562 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
f08cb5f2ffbe49601a9dc8cbb969460bf0b73eeb113fb6f02117ea36a4398216

Height

#113,196

Difficulty

9.730504

Transactions

3

Size

698 B

Version

2

Bits

09bb024a

Nonce

130,318

Timestamp

8/12/2013, 9:46:56 AM

Confirmations

6,713,562

Merkle Root

78a288bea660e9857b5051681a88ee1f39bf77e72b27e374a7be4ab0427aae7e
Transactions (3)
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.

2.758 × 10⁹⁷(98-digit number)
27587724716870288413…13622073043973558049
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.

1
origin − 1
2.758 × 10⁹⁷(98-digit number)
27587724716870288413…13622073043973558049
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
5.517 × 10⁹⁷(98-digit number)
55175449433740576826…27244146087947116099
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
1.103 × 10⁹⁸(99-digit number)
11035089886748115365…54488292175894232199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
2.207 × 10⁹⁸(99-digit number)
22070179773496230730…08976584351788464399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
4.414 × 10⁹⁸(99-digit number)
44140359546992461461…17953168703576928799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
8.828 × 10⁹⁸(99-digit number)
88280719093984922922…35906337407153857599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
1.765 × 10⁹⁹(100-digit number)
17656143818796984584…71812674814307715199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
3.531 × 10⁹⁹(100-digit number)
35312287637593969169…43625349628615430399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
7.062 × 10⁹⁹(100-digit number)
70624575275187938338…87250699257230860799
Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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, …
Circulating Supply:57,858,223 XPM·at block #6,826,757 · updates every 60s
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