XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #2,656,104

Block #2,656,104

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/10/2018, 6:38:42 PM Β· Difficulty 11.6960 Β· 4,186,287 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
13aaf5d0f8355fc71a80d342b354f4ff906e5b016e6be1c5dc9fb737c7e12bae
View on Chainz β†—

Difficulty

11.695967

Transactions

2

Size

835 B

Version

2

Bits

0bb22aea

Nonce

144,531,091

Timestamp

5/10/2018, 6:38:42 PM

Confirmations

4,186,287

Merkle Root

6569675a30a881e7322a579069494da59632cd74430ff6fba65f6fb601404b3a
Transactions (2)
Coinbasecdd9f93570746e…71b80bde25e0ad
1 in β†’ 1 out7.3100 XPM110 B
AMjb8Xek…LD6y1G4Q
226e257901cee4…41cce681cb7db5
4 in β†’ 2 out8.0223 XPM636 B
AUHBKKGB…mR5KpgvJAa6ZNCxL…GBZXzUbj
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.

2.412 Γ— 10⁹³(94-digit number)
24124651727333046079…86363113178179920000
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
2.412 Γ— 10⁹³(94-digit number)
24124651727333046079…86363113178179919999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.824 Γ— 10⁹³(94-digit number)
48249303454666092158…72726226356359839999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
9.649 Γ— 10⁹³(94-digit number)
96498606909332184316…45452452712719679999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.929 Γ— 10⁹⁴(95-digit number)
19299721381866436863…90904905425439359999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.859 Γ— 10⁹⁴(95-digit number)
38599442763732873726…81809810850878719999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
7.719 Γ— 10⁹⁴(95-digit number)
77198885527465747453…63619621701757439999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.543 Γ— 10⁹⁡(96-digit number)
15439777105493149490…27239243403514879999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.087 Γ— 10⁹⁡(96-digit number)
30879554210986298981…54478486807029759999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
6.175 Γ— 10⁹⁡(96-digit number)
61759108421972597962…08956973614059519999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.235 Γ— 10⁹⁢(97-digit number)
12351821684394519592…17913947228119039999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
2.470 Γ— 10⁹⁢(97-digit number)
24703643368789039185…35827894456238079999
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 First 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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 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 2656104

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 13aaf5d0f8355fc71a80d342b354f4ff906e5b016e6be1c5dc9fb737c7e12bae

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 #2,656,104 on Chainz β†—
Circulating Supply:57,983,538 XPMΒ·at block #6,842,390 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