XPM Prime Explorer symbol
XPMPrime Explorer

Block #2,638,448

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 4/30/2018, 7:07:45 AM Β· Difficulty 11.4927 Β· 4,198,681 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
500cfcf3e89063584e4342802eb79a22b06936b46cf8151244647c8a7c0e9380
View on Chainz β†—

Height

#2,638,448

Difficulty

11.492703

Transactions

1

Size

200 B

Version

2

Bits

0b7e21c5

Nonce

153,194,717

Timestamp

4/30/2018, 7:07:45 AM

Confirmations

4,198,681

Mined by

⛏️ P2SHALXFSvyxNKGtuNvPkY6i62xQGtCcUYVhmA

Merkle Root

3db22059859583e6818b52a2f7defeaf9685e63ca062adeeb4c27ef062daff12
Transactions (1)
Coinbase3db22059859583…c27ef062daff12
1 in β†’ 1 out7.5600 XPM110 B
ALXFSvyx…CcUYVhmA
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.

8.427 Γ— 10⁹⁡(96-digit number)
84274029323084517670…49432099513766996159
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
8.427 Γ— 10⁹⁡(96-digit number)
84274029323084517670…49432099513766996159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.685 Γ— 10⁹⁢(97-digit number)
16854805864616903534…98864199027533992319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.370 Γ— 10⁹⁢(97-digit number)
33709611729233807068…97728398055067984639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
6.741 Γ— 10⁹⁢(97-digit number)
67419223458467614136…95456796110135969279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.348 Γ— 10⁹⁷(98-digit number)
13483844691693522827…90913592220271938559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.696 Γ— 10⁹⁷(98-digit number)
26967689383387045654…81827184440543877119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
5.393 Γ— 10⁹⁷(98-digit number)
53935378766774091309…63654368881087754239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.078 Γ— 10⁹⁸(99-digit number)
10787075753354818261…27308737762175508479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.157 Γ— 10⁹⁸(99-digit number)
21574151506709636523…54617475524351016959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
4.314 Γ— 10⁹⁸(99-digit number)
43148303013419273047…09234951048702033919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
8.629 Γ— 10⁹⁸(99-digit number)
86296606026838546094…18469902097404067839
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 First 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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,941,341 XPMΒ·at block #6,837,128 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