XPM Prime Explorer symbol
XPMPrime Explorer

Block #2,640,142

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 4/30/2018, 9:46:09 PM Β· Difficulty 11.5686 Β· 4,204,414 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
abef676c6cdc3dce688cb3cf1ddf48e020cb9e2e950849b5cef61cfba870829b
View on Chainz β†—

Height

#2,640,142

Difficulty

11.568557

Transactions

1

Size

201 B

Version

2

Bits

0b918cf8

Nonce

98,617,134

Timestamp

4/30/2018, 9:46:09 PM

Confirmations

4,204,414

Mined by

⛏️ P2SHAdqah8zh3AxeLUnA13CQCRpLQc1WwoHJ9t

Merkle Root

33f7759ff8282b471446d9f10a3c1d6691af15ba9dabcfe669b1d047b1cdaf45
Transactions (1)
Coinbase33f7759ff8282b…b1d047b1cdaf45
1 in β†’ 1 out7.4600 XPM110 B
Adqah8zh…1WwoHJ9t
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.

2.266 Γ— 10⁹⁷(98-digit number)
22662841044483065665…07096768495547842561
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
2.266 Γ— 10⁹⁷(98-digit number)
22662841044483065665…07096768495547842561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.532 Γ— 10⁹⁷(98-digit number)
45325682088966131330…14193536991095685121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
9.065 Γ— 10⁹⁷(98-digit number)
90651364177932262661…28387073982191370241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.813 Γ— 10⁹⁸(99-digit number)
18130272835586452532…56774147964382740481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.626 Γ— 10⁹⁸(99-digit number)
36260545671172905064…13548295928765480961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
7.252 Γ— 10⁹⁸(99-digit number)
72521091342345810129…27096591857530961921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.450 Γ— 10⁹⁹(100-digit number)
14504218268469162025…54193183715061923841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.900 Γ— 10⁹⁹(100-digit number)
29008436536938324051…08386367430123847681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.801 Γ— 10⁹⁹(100-digit number)
58016873073876648103…16772734860247695361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.160 Γ— 10¹⁰⁰(101-digit number)
11603374614775329620…33545469720495390721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
2.320 Γ— 10¹⁰⁰(101-digit number)
23206749229550659241…67090939440990781441
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:58,000,851 XPMΒ·at block #6,844,555 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