XPM Prime Explorer symbol
XPMPrime Explorer

Block #2,778,443

2CCLength 12β˜…β˜…β˜…β˜…β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/4/2018, 6:17:52 AM Β· Difficulty 11.6506 Β· 4,062,635 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
8eec04b349e4c862b11baf274fedd40ec70cd248570e3b846392855e7439aeaa
View on Chainz β†—

Height

#2,778,443

Difficulty

11.650640

Transactions

2

Size

3.16 KB

Version

2

Bits

0ba6905e

Nonce

2,033,238,898

Timestamp

8/4/2018, 6:17:52 AM

Confirmations

4,062,635

Mined by

⛏️ P2SHALtQ32w14PXu4jYnZqgbBDabRaFG69SuYF

Merkle Root

bcc97afe57be32cd42de8cc0dda07749defe0eab8e47b90be2e3d54793903f23
Transactions (2)
Coinbase8579fc62ee540a…f930f3f9d82c0a
1 in β†’ 1 out7.3900 XPM110 B
ALtQ32w1…FG69SuYF
af3edbcb276a47…2298d0cb8d49c2
20 in β†’ 2 out190.8800 XPM2.96 KB
ALh5G3Np…6TsNC2wjAYfX4oYC…E55cPUs7
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.

8.392 Γ— 10⁹⁴(95-digit number)
83925094142834174239…32610667350127650561
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
8.392 Γ— 10⁹⁴(95-digit number)
83925094142834174239…32610667350127650561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.678 Γ— 10⁹⁡(96-digit number)
16785018828566834847…65221334700255301121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.357 Γ— 10⁹⁡(96-digit number)
33570037657133669695…30442669400510602241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.714 Γ— 10⁹⁡(96-digit number)
67140075314267339391…60885338801021204481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.342 Γ— 10⁹⁢(97-digit number)
13428015062853467878…21770677602042408961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.685 Γ— 10⁹⁢(97-digit number)
26856030125706935756…43541355204084817921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.371 Γ— 10⁹⁢(97-digit number)
53712060251413871513…87082710408169635841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.074 Γ— 10⁹⁷(98-digit number)
10742412050282774302…74165420816339271681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.148 Γ— 10⁹⁷(98-digit number)
21484824100565548605…48330841632678543361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.296 Γ— 10⁹⁷(98-digit number)
42969648201131097210…96661683265357086721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
8.593 Γ— 10⁹⁷(98-digit number)
85939296402262194420…93323366530714173441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
12
2^11 Γ— origin + 1
1.718 Γ— 10⁹⁸(99-digit number)
17187859280452438884…86646733061428346881
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 12 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
ExceptionalChain length 12

Around 1 in 10,000 blocks. A significant mathematical achievement.

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:57,972,986 XPMΒ·at block #6,841,077 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