XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #2,778,724

Block #2,778,724

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/4/2018, 11:16:42 AM Β· Difficulty 11.6492 Β· 4,060,627 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
1385477ddd6a5af6c389e7cc145ee654e0f167161663952e8a8004a24fa6ca48
View on Chainz β†—

Difficulty

11.649219

Transactions

1

Size

200 B

Version

2

Bits

0ba63331

Nonce

188,970,181

Timestamp

8/4/2018, 11:16:42 AM

Confirmations

4,060,627

Merkle Root

05a10335588d3ff492c780f95c18ed861793071bfa81fb63479ffb7ad54f3d20
Transactions (1)
Coinbase05a10335588d3f…9ffb7ad54f3d20
1 in β†’ 1 out7.3600 XPM109 B
Ab6fBN3K…95t2iNS4
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.

2.210 Γ— 10⁹⁷(98-digit number)
22104092093761705051…53581708231759708160
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
2.210 Γ— 10⁹⁷(98-digit number)
22104092093761705051…53581708231759708159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.420 Γ— 10⁹⁷(98-digit number)
44208184187523410102…07163416463519416319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
8.841 Γ— 10⁹⁷(98-digit number)
88416368375046820204…14326832927038832639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.768 Γ— 10⁹⁸(99-digit number)
17683273675009364040…28653665854077665279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.536 Γ— 10⁹⁸(99-digit number)
35366547350018728081…57307331708155330559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
7.073 Γ— 10⁹⁸(99-digit number)
70733094700037456163…14614663416310661119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.414 Γ— 10⁹⁹(100-digit number)
14146618940007491232…29229326832621322239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.829 Γ— 10⁹⁹(100-digit number)
28293237880014982465…58458653665242644479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
5.658 Γ— 10⁹⁹(100-digit number)
56586475760029964930…16917307330485288959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.131 Γ— 10¹⁰⁰(101-digit number)
11317295152005992986…33834614660970577919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
2.263 Γ— 10¹⁰⁰(101-digit number)
22634590304011985972…67669229321941155839
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 2778724

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 1385477ddd6a5af6c389e7cc145ee654e0f167161663952e8a8004a24fa6ca48

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 #2,778,724 on Chainz β†—
Circulating Supply:57,959,094 XPMΒ·at block #6,839,350 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