XPM Prime Explorer symbol
XPMPrime Explorer

Block #1,812,324

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 10/18/2016, 9:16:46 AM Β· Difficulty 10.7817 Β· 4,992,685 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
304ff88757259e0f8e69c256270853ef6a18fe80403d3fbbe54af1a25d3e8597
View on Chainz β†—

Height

#1,812,324

Difficulty

10.781658

Transactions

2

Size

2.00 KB

Version

2

Bits

0ac81ab7

Nonce

1,408,693,456

Timestamp

10/18/2016, 9:16:46 AM

Confirmations

4,992,685

Mined by

⛏️ P2SHAZ7wT6JJArg7UrVUhMPz1CBHyJVmnLCnA7

Merkle Root

78bad358d0a3d9c9bd3b5d04752b7d15172b40f4ae3dda8cda89ea2551b4c610
Transactions (2)
Coinbasec05b72454fc4ee…9324c3f85d9719
1 in β†’ 1 out8.6200 XPM109 B
AZ7wT6JJ…VmnLCnA7
1f85c1d169a7d2…40dc14913efb47
12 in β†’ 2 out50000.0100 XPM1.81 KB
AYKArr5V…V9VqiqCZAaCjsGsJ…aU9q6rkp
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.

1.186 Γ— 10⁹⁴(95-digit number)
11866007287563945002…35317564072727574401
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
1.186 Γ— 10⁹⁴(95-digit number)
11866007287563945002…35317564072727574401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.373 Γ— 10⁹⁴(95-digit number)
23732014575127890005…70635128145455148801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.746 Γ— 10⁹⁴(95-digit number)
47464029150255780010…41270256290910297601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
9.492 Γ— 10⁹⁴(95-digit number)
94928058300511560021…82540512581820595201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.898 Γ— 10⁹⁡(96-digit number)
18985611660102312004…65081025163641190401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.797 Γ— 10⁹⁡(96-digit number)
37971223320204624008…30162050327282380801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
7.594 Γ— 10⁹⁡(96-digit number)
75942446640409248017…60324100654564761601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.518 Γ— 10⁹⁢(97-digit number)
15188489328081849603…20648201309129523201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.037 Γ— 10⁹⁢(97-digit number)
30376978656163699206…41296402618259046401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
6.075 Γ— 10⁹⁢(97-digit number)
60753957312327398413…82592805236518092801
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:57,684,141 XPMΒ·at block #6,805,008 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.
AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK