XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #2,635,328

Block #2,635,328

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 4/29/2018, 5:19:42 AM Β· Difficulty 11.3071 Β· 4,195,927 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
8986c3e8327dd5950db5ef8ae6020d586f3567498beb4d444f2198e4627212a4
View on Chainz β†—

Difficulty

11.307130

Transactions

2

Size

426 B

Version

2

Bits

0b4ea018

Nonce

145,504,706

Timestamp

4/29/2018, 5:19:42 AM

Confirmations

4,195,927

Merkle Root

bbd89d673cb0b04c4c3f634b75841ef4cf1b99f9e1b9c351c85a4a0d9e313d42
Transactions (2)
Coinbase1f101e5633d05f…b1b11fee8bc423
1 in β†’ 1 out7.8200 XPM110 B
ATLBF8fW…E83NGJdj
bbef153185cf16…0ffa559099a8ce
1 in β†’ 2 out199790.3571 XPM225 B
ARGdyZaX…WjKp7YVmAHzkHzeK…3wME2gBF
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.

2.519 Γ— 10⁹⁢(97-digit number)
25194686096717656672…04589537328855710080
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
2.519 Γ— 10⁹⁢(97-digit number)
25194686096717656672…04589537328855710079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
5.038 Γ— 10⁹⁢(97-digit number)
50389372193435313344…09179074657711420159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.007 Γ— 10⁹⁷(98-digit number)
10077874438687062668…18358149315422840319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.015 Γ— 10⁹⁷(98-digit number)
20155748877374125337…36716298630845680639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.031 Γ— 10⁹⁷(98-digit number)
40311497754748250675…73432597261691361279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
8.062 Γ— 10⁹⁷(98-digit number)
80622995509496501351…46865194523382722559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.612 Γ— 10⁹⁸(99-digit number)
16124599101899300270…93730389046765445119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.224 Γ— 10⁹⁸(99-digit number)
32249198203798600540…87460778093530890239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
6.449 Γ— 10⁹⁸(99-digit number)
64498396407597201081…74921556187061780479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.289 Γ— 10⁹⁹(100-digit number)
12899679281519440216…49843112374123560959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
2.579 Γ— 10⁹⁹(100-digit number)
25799358563038880432…99686224748247121919
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 2635328

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 8986c3e8327dd5950db5ef8ae6020d586f3567498beb4d444f2198e4627212a4

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 #2,635,328 on Chainz β†—
Circulating Supply:57,894,190 XPMΒ·at block #6,831,254 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