XPM Prime Explorer symbol
XPMPrime Explorer

Block #1,681,482

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/20/2016, 9:23:22 AM Β· Difficulty 10.7154 Β· 5,160,025 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
7d92faddc44ed28a07578a3d7bedc6a7e5e1517c6b6b06c14c608d9534c780aa
View on Chainz β†—

Height

#1,681,482

Difficulty

10.715354

Transactions

1

Size

199 B

Version

2

Bits

0ab72173

Nonce

1,004,541,403

Timestamp

7/20/2016, 9:23:22 AM

Confirmations

5,160,025

Mined by

⛏️ P2SHAYxXPUvKwRse127m6yuJbuL7PA5pLtYqHf

Merkle Root

29dbb8965b7220ecc14739671a95740dc083d68d8dad20fcaa89117ab52b0642
Transactions (1)
Coinbase29dbb8965b7220…89117ab52b0642
1 in β†’ 1 out8.7000 XPM109 B
AYxXPUvK…5pLtYqHf
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.

3.251 Γ— 10⁹⁡(96-digit number)
32518253250886808148…59636045290573223359
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
3.251 Γ— 10⁹⁡(96-digit number)
32518253250886808148…59636045290573223359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
6.503 Γ— 10⁹⁡(96-digit number)
65036506501773616296…19272090581146446719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.300 Γ— 10⁹⁢(97-digit number)
13007301300354723259…38544181162292893439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.601 Γ— 10⁹⁢(97-digit number)
26014602600709446518…77088362324585786879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
5.202 Γ— 10⁹⁢(97-digit number)
52029205201418893037…54176724649171573759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.040 Γ— 10⁹⁷(98-digit number)
10405841040283778607…08353449298343147519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.081 Γ— 10⁹⁷(98-digit number)
20811682080567557214…16706898596686295039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.162 Γ— 10⁹⁷(98-digit number)
41623364161135114429…33413797193372590079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
8.324 Γ— 10⁹⁷(98-digit number)
83246728322270228859…66827594386745180159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.664 Γ— 10⁹⁸(99-digit number)
16649345664454045771…33655188773490360319
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:57,976,435 XPMΒ·at block #6,841,506 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