XPM Prime Explorer symbol
XPMPrime Explorer

Block #2,324,241

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 10/5/2017, 5:49:07 PM Β· Difficulty 10.9243 Β· 4,502,428 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
a62cc998641489223e4759b70814b8c05e94725c7e2f36a66fb3549fa73c46e1
View on Chainz β†—

Height

#2,324,241

Difficulty

10.924286

Transactions

2

Size

1.14 KB

Version

2

Bits

0aec9e02

Nonce

505,049,599

Timestamp

10/5/2017, 5:49:07 PM

Confirmations

4,502,428

Mined by

⛏️ P2SHAbTcyXKm1JHurrhUaYRfFpiqk89AkwCwmh

Merkle Root

46ed06471a35f8fe880ac633eb7d84d2d4240aeccd155668aabd20cefebe57f8
Transactions (2)
Coinbasebf6501493cc9bc…5fbf724c5a0373
1 in β†’ 1 out8.3800 XPM109 B
AbTcyXKm…9AkwCwmh
63e18dd17d08d5…949814670e9a38
6 in β†’ 2 out65.7812 XPM966 B
AXwjkaf2…eK7BjUNFAUbmGRu3…HPB8YEwK
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.

2.288 Γ— 10⁹⁴(95-digit number)
22884443162400162928…20533296457825669439
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
2.288 Γ— 10⁹⁴(95-digit number)
22884443162400162928…20533296457825669439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.576 Γ— 10⁹⁴(95-digit number)
45768886324800325857…41066592915651338879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
9.153 Γ— 10⁹⁴(95-digit number)
91537772649600651715…82133185831302677759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.830 Γ— 10⁹⁡(96-digit number)
18307554529920130343…64266371662605355519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.661 Γ— 10⁹⁡(96-digit number)
36615109059840260686…28532743325210711039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
7.323 Γ— 10⁹⁡(96-digit number)
73230218119680521372…57065486650421422079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.464 Γ— 10⁹⁢(97-digit number)
14646043623936104274…14130973300842844159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.929 Γ— 10⁹⁢(97-digit number)
29292087247872208548…28261946601685688319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
5.858 Γ— 10⁹⁢(97-digit number)
58584174495744417097…56523893203371376639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.171 Γ— 10⁹⁷(98-digit number)
11716834899148883419…13047786406742753279
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,857,499 XPMΒ·at block #6,826,668 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