XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #2,098,519

Block #2,098,519

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/3/2017, 4:28:12 PM Β· Difficulty 10.8632 Β· 4,743,640 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
e9ed8559f6c79cc154ec21def8740e26760d7fea124b2292c53fa9f15af63d7f
View on Chainz β†—

Difficulty

10.863198

Transactions

1

Size

199 B

Version

2

Bits

0adcfa8c

Nonce

473,392,897

Timestamp

5/3/2017, 4:28:12 PM

Confirmations

4,743,640

Merkle Root

6d52b0b4641f6cbf01b4ffa99581ab1e460c5a100e5c8a3b1b63a9b1d2c7f7d0
Transactions (1)
Coinbase6d52b0b4641f6c…63a9b1d2c7f7d0
1 in β†’ 1 out8.4600 XPM109 B
AULEmDzf…CPtXYB4n
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.

1.343 Γ— 10⁹⁴(95-digit number)
13439382832651129287…30923304251682160640
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
1.343 Γ— 10⁹⁴(95-digit number)
13439382832651129287…30923304251682160641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.687 Γ— 10⁹⁴(95-digit number)
26878765665302258575…61846608503364321281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
5.375 Γ— 10⁹⁴(95-digit number)
53757531330604517150…23693217006728642561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.075 Γ— 10⁹⁡(96-digit number)
10751506266120903430…47386434013457285121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.150 Γ— 10⁹⁡(96-digit number)
21503012532241806860…94772868026914570241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.300 Γ— 10⁹⁡(96-digit number)
43006025064483613720…89545736053829140481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
8.601 Γ— 10⁹⁡(96-digit number)
86012050128967227440…79091472107658280961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.720 Γ— 10⁹⁢(97-digit number)
17202410025793445488…58182944215316561921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.440 Γ— 10⁹⁢(97-digit number)
34404820051586890976…16365888430633123841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
6.880 Γ— 10⁹⁢(97-digit number)
68809640103173781952…32731776861266247681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.376 Γ— 10⁹⁷(98-digit number)
13761928020634756390…65463553722532495361
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 2098519

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 e9ed8559f6c79cc154ec21def8740e26760d7fea124b2292c53fa9f15af63d7f

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 #2,098,519 on Chainz β†—
Circulating Supply:57,981,663 XPMΒ·at block #6,842,158 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