XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #2,786,059

Block #2,786,059

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/9/2018, 7:46:49 AM Β· Difficulty 11.6727 Β· 4,058,747 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
c8140b4de58e71b7066ac8256f6d1345f9cb5ec7d9acf5a0df50d4a4485b5fac
View on Chainz β†—

Difficulty

11.672686

Transactions

1

Size

200 B

Version

2

Bits

0bac352d

Nonce

432,545,995

Timestamp

8/9/2018, 7:46:49 AM

Confirmations

4,058,747

Merkle Root

90f446ad18a169232cd8255566ef6f9c0a160b0b27822e014c3803be3baba87e
Transactions (1)
Coinbase90f446ad18a169…3803be3baba87e
1 in β†’ 1 out7.3300 XPM109 B
AGcxsHzQ…wx4TgGpu
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.

1.570 Γ— 10⁹⁢(97-digit number)
15701905127129769450…35881665219371315200
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
1.570 Γ— 10⁹⁢(97-digit number)
15701905127129769450…35881665219371315201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.140 Γ— 10⁹⁢(97-digit number)
31403810254259538900…71763330438742630401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
6.280 Γ— 10⁹⁢(97-digit number)
62807620508519077800…43526660877485260801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.256 Γ— 10⁹⁷(98-digit number)
12561524101703815560…87053321754970521601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.512 Γ— 10⁹⁷(98-digit number)
25123048203407631120…74106643509941043201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
5.024 Γ— 10⁹⁷(98-digit number)
50246096406815262240…48213287019882086401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.004 Γ— 10⁹⁸(99-digit number)
10049219281363052448…96426574039764172801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.009 Γ— 10⁹⁸(99-digit number)
20098438562726104896…92853148079528345601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.019 Γ— 10⁹⁸(99-digit number)
40196877125452209792…85706296159056691201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
8.039 Γ— 10⁹⁸(99-digit number)
80393754250904419584…71412592318113382401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.607 Γ— 10⁹⁹(100-digit number)
16078750850180883916…42825184636226764801
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.

View full Prime Chain Discovery page β†’
β˜…β˜…β˜…β˜†β˜†
Rarity
RareChain length 11
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, …
Verify on a Primecoin Node

Anyone running a Primecoin node can independently verify this block using the following RPC commands. Run these from the primecoin-cli command line or via the debug console in the Primecoin wallet.

1. Get block hash by height
getblockhash 2786059

Returns the block hash for a given block height. Use this to confirm the hash shown above matches the chain.

2. Get full block data
getblock c8140b4de58e71b7066ac8256f6d1345f9cb5ec7d9acf5a0df50d4a4485b5fac

Returns the full block header including difficulty, prime chain origin, prime chain type, transaction IDs, and all other fields shown on this page.

How to run these commands: To verify this data independently, open a terminal on your own Primecoin node and run primecoin-cli <command>. Alternatively, open the Primecoin-Qt wallet, go to Help β†’ Debug Window β†’ Console, and type the command directly. The node must be fully synced to this block height for the commands to return results.

Cross-reference on Chainz Explorer

Chainz is an independent Primecoin block explorer. Compare this block's data to verify accuracy.

View Block #2,786,059 on Chainz β†—
Circulating Supply:58,002,864 XPMΒ·at block #6,844,805 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