XPM Prime Explorer symbol
XPMPrime Explorer

Block #2,653,092

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/8/2018, 2:55:35 AM Β· Difficulty 11.7408 Β· 4,189,923 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
2ae5e7ae3533f0e17bd33ebc439586a36ccc958b6b28046b979a76829bd6109b
View on Chainz β†—

Height

#2,653,092

Difficulty

11.740806

Transactions

2

Size

721 B

Version

2

Bits

0bbda578

Nonce

1,457,589,286

Timestamp

5/8/2018, 2:55:35 AM

Confirmations

4,189,923

Mined by

⛏️ P2SHAHT6FGpCzAUCuKvF8yWdGLwbUK4VgwJe71

Merkle Root

79df153799d5c5344b1bbda0e88f3a9c1c7db8928ecdba25bc121287c5f517ea
Transactions (2)
Coinbase0ae31911da9b31…3a4c83c2007033
1 in β†’ 1 out7.2500 XPM110 B
AHT6FGpC…4VgwJe71
b10e22b962eea2…c5c68ee3ee213e
3 in β†’ 2 out890.2437 XPM521 B
AU7xkW52…RMPvkSaUAQvCF7bF…FVvquQYi
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.

1.426 Γ— 10⁹⁡(96-digit number)
14266272687639205266…10656262254039600001
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
1.426 Γ— 10⁹⁡(96-digit number)
14266272687639205266…10656262254039600001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.853 Γ— 10⁹⁡(96-digit number)
28532545375278410532…21312524508079200001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
5.706 Γ— 10⁹⁡(96-digit number)
57065090750556821064…42625049016158400001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.141 Γ— 10⁹⁢(97-digit number)
11413018150111364212…85250098032316800001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.282 Γ— 10⁹⁢(97-digit number)
22826036300222728425…70500196064633600001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.565 Γ— 10⁹⁢(97-digit number)
45652072600445456851…41000392129267200001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
9.130 Γ— 10⁹⁢(97-digit number)
91304145200890913702…82000784258534400001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.826 Γ— 10⁹⁷(98-digit number)
18260829040178182740…64001568517068800001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.652 Γ— 10⁹⁷(98-digit number)
36521658080356365481…28003137034137600001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
7.304 Γ— 10⁹⁷(98-digit number)
73043316160712730962…56006274068275200001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.460 Γ— 10⁹⁸(99-digit number)
14608663232142546192…12012548136550400001
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:57,988,475 XPMΒ·at block #6,843,014 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