Block #2,911,453

1CCLength 11★★★☆☆

Cunningham Chain of the First Kind · Discovered 11/5/2018, 6:02:44 PM · Difficulty 11.5253 · 3,931,573 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
f7815d93d3377271730f96f5746d5587c184b777836d6d24c7ac811eb1dbef0f

Height

#2,911,453

Difficulty

11.525317

Transactions

6

Size

1.94 KB

Version

2

Bits

0b867b30

Nonce

1,911,885,575

Timestamp

11/5/2018, 6:02:44 PM

Confirmations

3,931,573

Merkle Root

fbc89ecadacd0eb4baf418875af049788a3f1a88c29b17a8ab705452a8170c9d
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.

1.917 × 10⁹⁶(97-digit number)
19172124847953409132…60569014087173311999
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
1.917 × 10⁹⁶(97-digit number)
19172124847953409132…60569014087173311999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
3.834 × 10⁹⁶(97-digit number)
38344249695906818265…21138028174346623999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
7.668 × 10⁹⁶(97-digit number)
76688499391813636531…42276056348693247999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
1.533 × 10⁹⁷(98-digit number)
15337699878362727306…84552112697386495999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
3.067 × 10⁹⁷(98-digit number)
30675399756725454612…69104225394772991999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
6.135 × 10⁹⁷(98-digit number)
61350799513450909224…38208450789545983999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
1.227 × 10⁹⁸(99-digit number)
12270159902690181844…76416901579091967999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
2.454 × 10⁹⁸(99-digit number)
24540319805380363689…52833803158183935999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
4.908 × 10⁹⁸(99-digit number)
49080639610760727379…05667606316367871999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
9.816 × 10⁹⁸(99-digit number)
98161279221521454759…11335212632735743999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
11
2^10 × origin − 1
1.963 × 10⁹⁹(100-digit number)
19632255844304290951…22670425265471487999
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:57,988,562 XPM·at block #6,843,025 · 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