Block #2,748,009

1CCLength 11★★★☆☆

Cunningham Chain of the First Kind · Discovered 7/14/2018, 2:39:08 AM · Difficulty 11.6511 · 4,094,245 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
5d7a231e4785039f020ec482e805312fc61eae4d0410d00aa5bfedaa90fa1868

Height

#2,748,009

Difficulty

11.651087

Transactions

4

Size

1.30 KB

Version

2

Bits

0ba6ada4

Nonce

870,640,467

Timestamp

7/14/2018, 2:39:08 AM

Confirmations

4,094,245

Merkle Root

5ebc1bc455924b73d2c57fabc87f105c1dd4e7ebcf8a3565007a8126763f7bea
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.

4.465 × 10⁹⁴(95-digit number)
44658600665657559055…31246854416963949119
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
4.465 × 10⁹⁴(95-digit number)
44658600665657559055…31246854416963949119
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
8.931 × 10⁹⁴(95-digit number)
89317201331315118111…62493708833927898239
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
1.786 × 10⁹⁵(96-digit number)
17863440266263023622…24987417667855796479
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
3.572 × 10⁹⁵(96-digit number)
35726880532526047244…49974835335711592959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
7.145 × 10⁹⁵(96-digit number)
71453761065052094489…99949670671423185919
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
1.429 × 10⁹⁶(97-digit number)
14290752213010418897…99899341342846371839
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
2.858 × 10⁹⁶(97-digit number)
28581504426020837795…99798682685692743679
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
5.716 × 10⁹⁶(97-digit number)
57163008852041675591…99597365371385487359
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
1.143 × 10⁹⁷(98-digit number)
11432601770408335118…99194730742770974719
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
2.286 × 10⁹⁷(98-digit number)
22865203540816670236…98389461485541949439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
11
2^10 × origin − 1
4.573 × 10⁹⁷(98-digit number)
45730407081633340472…96778922971083898879
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:57,982,429 XPM·at block #6,842,253 · updates every 60s
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