XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #2,850,469

Block #2,850,469

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/22/2018, 9:59:16 AM Β· Difficulty 11.7291 Β· 3,992,417 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
8a32a102ffad2e1180f935f10b438c481bc01fa3a0a9d50019a649afe1d5a35e
View on Chainz β†—

Difficulty

11.729148

Transactions

1

Size

201 B

Version

2

Bits

0bbaa973

Nonce

2,090,682,961

Timestamp

9/22/2018, 9:59:16 AM

Confirmations

3,992,417

Merkle Root

b9cf37f43c62892abe853f2c8221bba4b7d3ef80066672f32cd0831f85742be6
Transactions (1)
Coinbaseb9cf37f43c6289…d0831f85742be6
1 in β†’ 1 out7.2600 XPM110 B
AQXvbRbc…yyY6yMap
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.

7.807 Γ— 10⁹⁷(98-digit number)
78074278937481381134…16911110755297484800
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
7.807 Γ— 10⁹⁷(98-digit number)
78074278937481381134…16911110755297484799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.561 Γ— 10⁹⁸(99-digit number)
15614855787496276226…33822221510594969599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.122 Γ— 10⁹⁸(99-digit number)
31229711574992552453…67644443021189939199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
6.245 Γ— 10⁹⁸(99-digit number)
62459423149985104907…35288886042379878399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.249 Γ— 10⁹⁹(100-digit number)
12491884629997020981…70577772084759756799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.498 Γ— 10⁹⁹(100-digit number)
24983769259994041963…41155544169519513599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.996 Γ— 10⁹⁹(100-digit number)
49967538519988083926…82311088339039027199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
9.993 Γ— 10⁹⁹(100-digit number)
99935077039976167852…64622176678078054399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.998 Γ— 10¹⁰⁰(101-digit number)
19987015407995233570…29244353356156108799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.997 Γ— 10¹⁰⁰(101-digit number)
39974030815990467140…58488706712312217599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
7.994 Γ— 10¹⁰⁰(101-digit number)
79948061631980934281…16977413424624435199
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 2850469

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 8a32a102ffad2e1180f935f10b438c481bc01fa3a0a9d50019a649afe1d5a35e

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 #2,850,469 on Chainz β†—
Circulating Supply:57,987,434 XPMΒ·at block #6,842,885 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