XPM Prime Explorer symbol
XPMPrime Explorer

Block #2,866,623

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 10/4/2018, 8:32:06 AM Β· Difficulty 11.6677 Β· 3,975,544 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
52d2a42e3971647393a8a00db420c7909ad9593f6be894225d2b942850ca1c05
View on Chainz β†—

Height

#2,866,623

Difficulty

11.667739

Transactions

1

Size

201 B

Version

2

Bits

0baaf0ea

Nonce

340,680,774

Timestamp

10/4/2018, 8:32:06 AM

Confirmations

3,975,544

Mined by

⛏️ P2SHAGycK9CJiQBRCvgR8QnbrpxXV8FGV1B9J3

Merkle Root

e9212e6a2a1d4ad7e960144dc6664e102b0b263fd2cd8dcbb20a28ae8ada5b97
Transactions (1)
Coinbasee9212e6a2a1d4a…0a28ae8ada5b97
1 in β†’ 1 out7.3300 XPM110 B
AGycK9CJ…FGV1B9J3
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

1.316 Γ— 10⁹⁷(98-digit number)
13168212205721338728…21587490895179141121
Discovered Prime Numbers
p_k = 2^k Γ— 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
1.316 Γ— 10⁹⁷(98-digit number)
13168212205721338728…21587490895179141121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.633 Γ— 10⁹⁷(98-digit number)
26336424411442677456…43174981790358282241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
5.267 Γ— 10⁹⁷(98-digit number)
52672848822885354913…86349963580716564481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.053 Γ— 10⁹⁸(99-digit number)
10534569764577070982…72699927161433128961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.106 Γ— 10⁹⁸(99-digit number)
21069139529154141965…45399854322866257921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.213 Γ— 10⁹⁸(99-digit number)
42138279058308283931…90799708645732515841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
8.427 Γ— 10⁹⁸(99-digit number)
84276558116616567862…81599417291465031681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.685 Γ— 10⁹⁹(100-digit number)
16855311623323313572…63198834582930063361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.371 Γ— 10⁹⁹(100-digit number)
33710623246646627144…26397669165860126721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
6.742 Γ— 10⁹⁹(100-digit number)
67421246493293254289…52795338331720253441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.348 Γ— 10¹⁰⁰(101-digit number)
13484249298658650857…05590676663440506881
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 consecutive prime numbers forming a Cunningham Chain of the Second Kind. The prime chain origin β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

β˜…β˜…β˜…β˜†β˜†
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 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” those factors are the primorial divisor. The chain then extends from the first prime using the 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,981,727 XPMΒ·at block #6,842,166 Β· 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 PolicyΒ·
AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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.

Β·Privacy Policy