Block #2,680,929

1CCLength 11★★★☆☆

Cunningham Chain of the First Kind · Discovered 5/28/2018, 1:30:26 AM · Difficulty 11.6924 · 4,161,618 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
6509069dbdb0f15b8d2c9ab51c1914ea711e57ef3d389b40232edfb0f3582eb1

Height

#2,680,929

Difficulty

11.692442

Transactions

2

Size

426 B

Version

2

Bits

0bb143e6

Nonce

902,273,612

Timestamp

5/28/2018, 1:30:26 AM

Confirmations

4,161,618

Merkle Root

414ee6b719f7d5fa234e77a68baeb411bf8db41c48396c030fa4022348f827db
Transactions (2)
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.

4.479 × 10⁹⁵(96-digit number)
44798939402826218779…47871012542783020799
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
4.479 × 10⁹⁵(96-digit number)
44798939402826218779…47871012542783020799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
8.959 × 10⁹⁵(96-digit number)
89597878805652437559…95742025085566041599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
1.791 × 10⁹⁶(97-digit number)
17919575761130487511…91484050171132083199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
3.583 × 10⁹⁶(97-digit number)
35839151522260975023…82968100342264166399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
7.167 × 10⁹⁶(97-digit number)
71678303044521950047…65936200684528332799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
1.433 × 10⁹⁷(98-digit number)
14335660608904390009…31872401369056665599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
2.867 × 10⁹⁷(98-digit number)
28671321217808780019…63744802738113331199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
5.734 × 10⁹⁷(98-digit number)
57342642435617560038…27489605476226662399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
1.146 × 10⁹⁸(99-digit number)
11468528487123512007…54979210952453324799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
2.293 × 10⁹⁸(99-digit number)
22937056974247024015…09958421904906649599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
11
2^10 × origin − 1
4.587 × 10⁹⁸(99-digit number)
45874113948494048030…19916843809813299199
Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,984,801 XPM·at block #6,842,546 · updates every 60s
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