XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #2,826,942

Block #2,826,942

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/6/2018, 7:23:29 AM Β· Difficulty 11.7100 Β· 4,006,941 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
853418f2070736f9c009e1f969f1f0e8cd368c561472e0e07af1feea23d1d2dc
View on Chainz β†—

Difficulty

11.710012

Transactions

2

Size

60.78 KB

Version

2

Bits

0bb5c358

Nonce

547,266,869

Timestamp

9/6/2018, 7:23:29 AM

Confirmations

4,006,941

Merkle Root

c36725a8639fe729ff9ccb5738786835baa06645b12a7e282a88c86abe9fec4c
Transactions (2)
Coinbaseb9e1fc54e2624f…4c43578a6daa79
1 in β†’ 1 out7.9100 XPM110 B
AJL4qvzg…brUC2nYd
5a6e70cf9d27c6…796332519862a3
420 in β†’ 2 out1691.9017 XPM60.59 KB
AM5E5on2…gU3zA55RAJLeo6ui…Hmeg6Vkx
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.

6.806 Γ— 10⁹⁡(96-digit number)
68065087206623045269…59542170128058869760
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
6.806 Γ— 10⁹⁡(96-digit number)
68065087206623045269…59542170128058869761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.361 Γ— 10⁹⁢(97-digit number)
13613017441324609053…19084340256117739521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.722 Γ— 10⁹⁢(97-digit number)
27226034882649218107…38168680512235479041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.445 Γ— 10⁹⁢(97-digit number)
54452069765298436215…76337361024470958081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.089 Γ— 10⁹⁷(98-digit number)
10890413953059687243…52674722048941916161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.178 Γ— 10⁹⁷(98-digit number)
21780827906119374486…05349444097883832321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.356 Γ— 10⁹⁷(98-digit number)
43561655812238748972…10698888195767664641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
8.712 Γ— 10⁹⁷(98-digit number)
87123311624477497945…21397776391535329281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.742 Γ— 10⁹⁸(99-digit number)
17424662324895499589…42795552783070658561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.484 Γ— 10⁹⁸(99-digit number)
34849324649790999178…85591105566141317121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
6.969 Γ— 10⁹⁸(99-digit number)
69698649299581998356…71182211132282634241
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 2826942

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 853418f2070736f9c009e1f969f1f0e8cd368c561472e0e07af1feea23d1d2dc

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 #2,826,942 on Chainz β†—
Circulating Supply:57,915,295 XPMΒ·at block #6,833,882 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