XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #2,661,925

Block #2,661,925

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/15/2018, 10:33:00 AM Β· Difficulty 11.6370 Β· 4,177,861 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
9cb04022d2a6e44dd6beebdc524fbb22d7086fa5541d2fc2775f6f20e9e3043d
View on Chainz β†—

Difficulty

11.636972

Transactions

2

Size

871 B

Version

2

Bits

0ba31092

Nonce

1,310,376,006

Timestamp

5/15/2018, 10:33:00 AM

Confirmations

4,177,861

Merkle Root

e27f590856338ce9379d7edead75fa1df495666a83221db0f6fbf45927a651a2
Transactions (2)
Coinbaseb96fa23121376c…31d1f80a030509
1 in β†’ 1 out7.3800 XPM109 B
Adqah8zh…1WwoHJ9t
f6af7008372266…f820cf21e02f86
4 in β†’ 2 out9937.8700 XPM671 B
ANfHnS6i…cmJ5JwZUALssV9Qd…PvJB43wd
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.

5.945 Γ— 10⁹⁡(96-digit number)
59453303569978131699…45886838282388368320
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
5.945 Γ— 10⁹⁡(96-digit number)
59453303569978131699…45886838282388368321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.189 Γ— 10⁹⁢(97-digit number)
11890660713995626339…91773676564776736641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.378 Γ— 10⁹⁢(97-digit number)
23781321427991252679…83547353129553473281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.756 Γ— 10⁹⁢(97-digit number)
47562642855982505359…67094706259106946561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
9.512 Γ— 10⁹⁢(97-digit number)
95125285711965010719…34189412518213893121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.902 Γ— 10⁹⁷(98-digit number)
19025057142393002143…68378825036427786241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.805 Γ— 10⁹⁷(98-digit number)
38050114284786004287…36757650072855572481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
7.610 Γ— 10⁹⁷(98-digit number)
76100228569572008575…73515300145711144961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.522 Γ— 10⁹⁸(99-digit number)
15220045713914401715…47030600291422289921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.044 Γ— 10⁹⁸(99-digit number)
30440091427828803430…94061200582844579841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
6.088 Γ— 10⁹⁸(99-digit number)
60880182855657606860…88122401165689159681
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 2661925

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 9cb04022d2a6e44dd6beebdc524fbb22d7086fa5541d2fc2775f6f20e9e3043d

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 #2,661,925 on Chainz β†—
Circulating Supply:57,962,579 XPMΒ·at block #6,839,785 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