XPM Prime Explorer symbol
XPMPrime Explorer

Block #2,645,290

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/2/2018, 8:33:25 PM Β· Difficulty 11.7290 Β· 4,185,641 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
8149ca2b54cc5026e0ffc5e7d8aea9db3d358dc738eb7f1d0ed7cacd0fd86e67
View on Chainz β†—

Height

#2,645,290

Difficulty

11.729012

Transactions

2

Size

575 B

Version

2

Bits

0bbaa08c

Nonce

405,456,603

Timestamp

5/2/2018, 8:33:25 PM

Confirmations

4,185,641

Mined by

⛏️ P2SHAdqah8zh3AxeLUnA13CQCRpLQc1WwoHJ9t

Merkle Root

4578868e3db77dff9d90d52b0405e962e45c965f6c18fc196649f9530b823f4c
Transactions (2)
Coinbase0a3be06739a9b8…9c7e129e70a344
1 in β†’ 1 out7.2700 XPM110 B
Adqah8zh…1WwoHJ9t
2273714b8f2ff6…10cf3adb4e7c61
2 in β†’ 2 out1.0109 XPM375 B
ALzx5vd1…pEo3w8uoALkJSjhT…YgcTtWyc
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.

7.107 Γ— 10⁹⁡(96-digit number)
71070113470312758319…22095692104160440961
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
7.107 Γ— 10⁹⁡(96-digit number)
71070113470312758319…22095692104160440961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.421 Γ— 10⁹⁢(97-digit number)
14214022694062551663…44191384208320881921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.842 Γ— 10⁹⁢(97-digit number)
28428045388125103327…88382768416641763841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.685 Γ— 10⁹⁢(97-digit number)
56856090776250206655…76765536833283527681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.137 Γ— 10⁹⁷(98-digit number)
11371218155250041331…53531073666567055361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.274 Γ— 10⁹⁷(98-digit number)
22742436310500082662…07062147333134110721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.548 Γ— 10⁹⁷(98-digit number)
45484872621000165324…14124294666268221441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
9.096 Γ— 10⁹⁷(98-digit number)
90969745242000330648…28248589332536442881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.819 Γ— 10⁹⁸(99-digit number)
18193949048400066129…56497178665072885761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.638 Γ— 10⁹⁸(99-digit number)
36387898096800132259…12994357330145771521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
7.277 Γ— 10⁹⁸(99-digit number)
72775796193600264518…25988714660291543041
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:57,891,581 XPMΒ·at block #6,830,930 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