Block #2,139,425

1CCLength 11★★★☆☆

Cunningham Chain of the First Kind · Discovered 5/31/2017, 4:51:50 PM · Difficulty 10.8792 · 4,703,362 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
5664abd934aacb7bb00fee3de3b4381abd8c68b0cf69f9e1f382b71d23373486

Height

#2,139,425

Difficulty

10.879248

Transactions

3

Size

1.36 KB

Version

2

Bits

0ae1165e

Nonce

233,106,771

Timestamp

5/31/2017, 4:51:50 PM

Confirmations

4,703,362

Merkle Root

c1597b074fed893e48f9ae2493ca7036ba5441a6c6d574d970ff9f4617e5c4e3
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.

8.578 × 10⁹³(94-digit number)
85780740776155382371…27372316952239700079
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
8.578 × 10⁹³(94-digit number)
85780740776155382371…27372316952239700079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
1.715 × 10⁹⁴(95-digit number)
17156148155231076474…54744633904479400159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
3.431 × 10⁹⁴(95-digit number)
34312296310462152948…09489267808958800319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
6.862 × 10⁹⁴(95-digit number)
68624592620924305897…18978535617917600639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
1.372 × 10⁹⁵(96-digit number)
13724918524184861179…37957071235835201279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
2.744 × 10⁹⁵(96-digit number)
27449837048369722358…75914142471670402559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
5.489 × 10⁹⁵(96-digit number)
54899674096739444717…51828284943340805119
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
1.097 × 10⁹⁶(97-digit number)
10979934819347888943…03656569886681610239
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
2.195 × 10⁹⁶(97-digit number)
21959869638695777887…07313139773363220479
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
4.391 × 10⁹⁶(97-digit number)
43919739277391555774…14626279546726440959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
11
2^10 × origin − 1
8.783 × 10⁹⁶(97-digit number)
87839478554783111548…29252559093452881919
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:57,986,636 XPM·at block #6,842,786 · updates every 60s
xpmprime.info is a work in progress. If you enjoy using this service you can support this project with a Primecoin donation.
Privacy Policy·

Cookie Preferences

We use cookies to enhance your experience. Some are essential for the site to function, while others help us understand how you use the site.

·Privacy Policy