XPM Prime Explorer symbol
XPMPrime Explorer

Block #2,668,905

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/19/2018, 9:09:30 PM Β· Difficulty 11.6768 Β· 4,170,596 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
6599993178b00cab2dbf5ea54a0fae5723eb0131dcbe832c56e87865fee45e73
View on Chainz β†—

Height

#2,668,905

Difficulty

11.676826

Transactions

1

Size

201 B

Version

2

Bits

0bad447b

Nonce

938,052,225

Timestamp

5/19/2018, 9:09:30 PM

Confirmations

4,170,596

Mined by

⛏️ P2SHAQ28A8nLugo5nwC89Tikrfk9DeXJr1AcHE

Merkle Root

19f7576d3ffe6ef2bb98f5ac0b3519784aebfc0c894490d31151a75b069053d6
Transactions (1)
Coinbase19f7576d3ffe6e…51a75b069053d6
1 in β†’ 1 out7.3200 XPM110 B
AQ28A8nL…XJr1AcHE
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.

6.710 Γ— 10⁹⁷(98-digit number)
67108581792121544907…14649367850198323201
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
6.710 Γ— 10⁹⁷(98-digit number)
67108581792121544907…14649367850198323201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.342 Γ— 10⁹⁸(99-digit number)
13421716358424308981…29298735700396646401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.684 Γ— 10⁹⁸(99-digit number)
26843432716848617963…58597471400793292801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.368 Γ— 10⁹⁸(99-digit number)
53686865433697235926…17194942801586585601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.073 Γ— 10⁹⁹(100-digit number)
10737373086739447185…34389885603173171201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.147 Γ— 10⁹⁹(100-digit number)
21474746173478894370…68779771206346342401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.294 Γ— 10⁹⁹(100-digit number)
42949492346957788740…37559542412692684801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
8.589 Γ— 10⁹⁹(100-digit number)
85898984693915577481…75119084825385369601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.717 Γ— 10¹⁰⁰(101-digit number)
17179796938783115496…50238169650770739201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.435 Γ— 10¹⁰⁰(101-digit number)
34359593877566230992…00476339301541478401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
6.871 Γ— 10¹⁰⁰(101-digit number)
68719187755132461985…00952678603082956801
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:57,960,305 XPMΒ·at block #6,839,500 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