XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #2,804,775

Block #2,804,775

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/22/2018, 9:21:23 AM Β· Difficulty 11.6669 Β· 4,037,285 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
16f07afcf5588fef2245c6cb7e7bd8c0d7c6198948d98d45f43310f4a3376aff
View on Chainz β†—

Difficulty

11.666892

Transactions

2

Size

1.83 KB

Version

2

Bits

0baab96d

Nonce

1,190,427,789

Timestamp

8/22/2018, 9:21:23 AM

Confirmations

4,037,285

Merkle Root

adfdcb603c24be3405377977b19ef4c2a5b53c391520a105ae01d03929ecf6b4
Transactions (2)
Coinbase70f94dc30d1b83…9045136040664f
1 in β†’ 1 out7.3500 XPM110 B
AJoGjNma…aJKUf5cX
c8439b18b43f49…05575dd7664f55
11 in β†’ 1 out40.0000 XPM1.64 KB
AQRn6yfR…z5FsKtdj
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.

6.084 Γ— 10⁹⁢(97-digit number)
60847111308838339378…25883928981446144000
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
6.084 Γ— 10⁹⁢(97-digit number)
60847111308838339378…25883928981446143999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.216 Γ— 10⁹⁷(98-digit number)
12169422261767667875…51767857962892287999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.433 Γ— 10⁹⁷(98-digit number)
24338844523535335751…03535715925784575999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.867 Γ— 10⁹⁷(98-digit number)
48677689047070671502…07071431851569151999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
9.735 Γ— 10⁹⁷(98-digit number)
97355378094141343005…14142863703138303999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.947 Γ— 10⁹⁸(99-digit number)
19471075618828268601…28285727406276607999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.894 Γ— 10⁹⁸(99-digit number)
38942151237656537202…56571454812553215999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
7.788 Γ— 10⁹⁸(99-digit number)
77884302475313074404…13142909625106431999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.557 Γ— 10⁹⁹(100-digit number)
15576860495062614880…26285819250212863999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.115 Γ— 10⁹⁹(100-digit number)
31153720990125229761…52571638500425727999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
6.230 Γ— 10⁹⁹(100-digit number)
62307441980250459523…05143277000851455999
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 2804775

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 16f07afcf5588fef2245c6cb7e7bd8c0d7c6198948d98d45f43310f4a3376aff

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 #2,804,775 on Chainz β†—
Circulating Supply:57,980,862 XPMΒ·at block #6,842,059 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