XPM Prime Explorer symbol
XPMPrime Explorer

Block #2,162,449

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 6/16/2017, 12:40:45 AM Β· Difficulty 10.9008 Β· 4,669,275 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
188cde8a2a19290e396fe74d32e3dea3a3e97deb613298bc1b7605dd47aaf5d4
View on Chainz β†—

Height

#2,162,449

Difficulty

10.900761

Transactions

2

Size

3.56 KB

Version

2

Bits

0ae69841

Nonce

165,984,431

Timestamp

6/16/2017, 12:40:45 AM

Confirmations

4,669,275

Mined by

⛏️ P2SHAGoCvBMZ51S4dPw1j2rgiMU9P8tYUXkAnk

Merkle Root

34360ce431757868a42f3c8ace233af2de1274c905c2d27bf108087ddca62e6b
Transactions (2)
Coinbase98ac3813832dd1…af49e8d5783bb3
1 in β†’ 1 out8.4400 XPM109 B
AGoCvBMZ…tYUXkAnk
274b106ec007f1…3a6bb90819e4ba
23 in β†’ 1 out1578.9900 XPM3.37 KB
AcxhUhX6…N8N8w2tm
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.

6.670 Γ— 10⁹³(94-digit number)
66704089794880370888…73179054460546168799
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
6.670 Γ— 10⁹³(94-digit number)
66704089794880370888…73179054460546168799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.334 Γ— 10⁹⁴(95-digit number)
13340817958976074177…46358108921092337599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.668 Γ— 10⁹⁴(95-digit number)
26681635917952148355…92716217842184675199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.336 Γ— 10⁹⁴(95-digit number)
53363271835904296710…85432435684369350399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.067 Γ— 10⁹⁡(96-digit number)
10672654367180859342…70864871368738700799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.134 Γ— 10⁹⁡(96-digit number)
21345308734361718684…41729742737477401599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.269 Γ— 10⁹⁡(96-digit number)
42690617468723437368…83459485474954803199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
8.538 Γ— 10⁹⁡(96-digit number)
85381234937446874737…66918970949909606399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.707 Γ— 10⁹⁢(97-digit number)
17076246987489374947…33837941899819212799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.415 Γ— 10⁹⁢(97-digit number)
34152493974978749895…67675883799638425599
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:57,897,897 XPMΒ·at block #6,831,723 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