XPM Prime Explorer symbol
XPMPrime Explorer

Block #2,794,997

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/15/2018, 11:29:41 AM Β· Difficulty 11.6778 Β· 4,046,908 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
527b29c259e67fd7edced6028031439e6a93bd4fcd24c5255337e5c849331045
View on Chainz β†—

Height

#2,794,997

Difficulty

11.677809

Transactions

1

Size

199 B

Version

2

Bits

0bad84eb

Nonce

201,589,172

Timestamp

8/15/2018, 11:29:41 AM

Confirmations

4,046,908

Mined by

⛏️ P2SHAKCEWX63RFCz6AobJhujuMdpB9ktLnMYqJ

Merkle Root

f64a2abe85ad64cd828e6377ab236444db806f2b52e9afee650e3e105eecd3ed
Transactions (1)
Coinbasef64a2abe85ad64…0e3e105eecd3ed
1 in β†’ 1 out7.3200 XPM110 B
AKCEWX63…ktLnMYqJ
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.

2.576 Γ— 10⁹²(93-digit number)
25764052482953263326…28426196705607331841
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
2.576 Γ— 10⁹²(93-digit number)
25764052482953263326…28426196705607331841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.152 Γ— 10⁹²(93-digit number)
51528104965906526653…56852393411214663681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.030 Γ— 10⁹³(94-digit number)
10305620993181305330…13704786822429327361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.061 Γ— 10⁹³(94-digit number)
20611241986362610661…27409573644858654721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.122 Γ— 10⁹³(94-digit number)
41222483972725221323…54819147289717309441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
8.244 Γ— 10⁹³(94-digit number)
82444967945450442646…09638294579434618881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.648 Γ— 10⁹⁴(95-digit number)
16488993589090088529…19276589158869237761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.297 Γ— 10⁹⁴(95-digit number)
32977987178180177058…38553178317738475521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
6.595 Γ— 10⁹⁴(95-digit number)
65955974356360354117…77106356635476951041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.319 Γ— 10⁹⁡(96-digit number)
13191194871272070823…54212713270953902081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
2.638 Γ— 10⁹⁡(96-digit number)
26382389742544141646…08425426541907804161
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 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
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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,979,614 XPMΒ·at block #6,841,904 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