XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #2,838,109

Block #2,838,109

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/13/2018, 11:19:53 PM Β· Difficulty 11.7177 Β· 4,003,681 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
2c8dd4ea6deeeedee7f07449847bcc63d8a3d3e3ca4a8f405d415880eed50c96
View on Chainz β†—

Difficulty

11.717697

Transactions

1

Size

200 B

Version

2

Bits

0bb7baf7

Nonce

72,412,977

Timestamp

9/13/2018, 11:19:53 PM

Confirmations

4,003,681

Merkle Root

bcc4ac1e21d5c4cb0a39a8cc001f7bfa21fc3cd391284d7a5e764c20c550d9b0
Transactions (1)
Coinbasebcc4ac1e21d5c4…764c20c550d9b0
1 in β†’ 1 out7.2700 XPM110 B
AGAPWA3H…SVubMULi
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.

5.590 Γ— 10⁹⁴(95-digit number)
55907402123580969349…06655636447016022560
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
5.590 Γ— 10⁹⁴(95-digit number)
55907402123580969349…06655636447016022559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.118 Γ— 10⁹⁡(96-digit number)
11181480424716193869…13311272894032045119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.236 Γ— 10⁹⁡(96-digit number)
22362960849432387739…26622545788064090239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.472 Γ— 10⁹⁡(96-digit number)
44725921698864775479…53245091576128180479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
8.945 Γ— 10⁹⁡(96-digit number)
89451843397729550958…06490183152256360959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.789 Γ— 10⁹⁢(97-digit number)
17890368679545910191…12980366304512721919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.578 Γ— 10⁹⁢(97-digit number)
35780737359091820383…25960732609025443839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
7.156 Γ— 10⁹⁢(97-digit number)
71561474718183640767…51921465218050887679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.431 Γ— 10⁹⁷(98-digit number)
14312294943636728153…03842930436101775359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.862 Γ— 10⁹⁷(98-digit number)
28624589887273456306…07685860872203550719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
5.724 Γ— 10⁹⁷(98-digit number)
57249179774546912613…15371721744407101439
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 2838109

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 2c8dd4ea6deeeedee7f07449847bcc63d8a3d3e3ca4a8f405d415880eed50c96

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 #2,838,109 on Chainz β†—
Circulating Supply:57,978,698 XPMΒ·at block #6,841,789 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