XPM Prime Explorer symbol
XPMPrime Explorer

Block #2,131,914

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/25/2017, 10:38:17 AM Β· Difficulty 10.9101 Β· 4,710,507 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
cbdad7cc2995e8e477a9e3ddc0f1e198e070f28cbe44dd0993123ad61310ba70
View on Chainz β†—

Height

#2,131,914

Difficulty

10.910143

Transactions

1

Size

199 B

Version

2

Bits

0ae8ff1c

Nonce

230,073,501

Timestamp

5/25/2017, 10:38:17 AM

Confirmations

4,710,507

Mined by

⛏️ P2SHAdQVboXsyzuYCiGi6isEhHNwemhwJk4NqM

Merkle Root

570d5e03dc2ef3bdbf749c1edc501084dfaa96f198051fc3f92809a4ca96150d
Transactions (1)
Coinbase570d5e03dc2ef3…2809a4ca96150d
1 in β†’ 1 out8.3900 XPM109 B
AdQVboXs…hwJk4NqM
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.

1.147 Γ— 10⁹⁴(95-digit number)
11471375923385307143…69795394427222939561
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
1.147 Γ— 10⁹⁴(95-digit number)
11471375923385307143…69795394427222939561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.294 Γ— 10⁹⁴(95-digit number)
22942751846770614286…39590788854445879121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.588 Γ— 10⁹⁴(95-digit number)
45885503693541228572…79181577708891758241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
9.177 Γ— 10⁹⁴(95-digit number)
91771007387082457144…58363155417783516481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.835 Γ— 10⁹⁡(96-digit number)
18354201477416491428…16726310835567032961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.670 Γ— 10⁹⁡(96-digit number)
36708402954832982857…33452621671134065921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
7.341 Γ— 10⁹⁡(96-digit number)
73416805909665965715…66905243342268131841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.468 Γ— 10⁹⁢(97-digit number)
14683361181933193143…33810486684536263681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.936 Γ— 10⁹⁢(97-digit number)
29366722363866386286…67620973369072527361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.873 Γ— 10⁹⁢(97-digit number)
58733444727732772572…35241946738145054721
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 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
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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,983,782 XPMΒ·at block #6,842,420 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