XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #516,911

Block #516,911

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 4/29/2014, 3:19:02 PM Β· Difficulty 10.8494 Β· 6,316,271 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
e09f8d2b1841f872c9d64798818dda4eb03825ae9be76b5e5bed0be93ae2a0b7
View on Chainz β†—

Height

#516,911

Difficulty

10.849395

Transactions

1

Size

202 B

Version

2

Bits

0ad971fb

Nonce

240,820,772

Timestamp

4/29/2014, 3:19:02 PM

Confirmations

6,316,271

Merkle Root

d1001a9ed75df43845e4a2a527afe892540a12f2ecde9355dcbcfa4dad8846a9
Transactions (1)
Coinbased1001a9ed75df4…bcfa4dad8846a9
1 in β†’ 1 out8.4800 XPM110 B
AX2UMEpf…Mr2T2Gma
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.

2.019 Γ— 10⁹⁸(99-digit number)
20191193155500271235…69564512755171016000
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
2.019 Γ— 10⁹⁸(99-digit number)
20191193155500271235…69564512755171015999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.038 Γ— 10⁹⁸(99-digit number)
40382386311000542470…39129025510342031999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
8.076 Γ— 10⁹⁸(99-digit number)
80764772622001084940…78258051020684063999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.615 Γ— 10⁹⁹(100-digit number)
16152954524400216988…56516102041368127999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.230 Γ— 10⁹⁹(100-digit number)
32305909048800433976…13032204082736255999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
6.461 Γ— 10⁹⁹(100-digit number)
64611818097600867952…26064408165472511999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.292 Γ— 10¹⁰⁰(101-digit number)
12922363619520173590…52128816330945023999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.584 Γ— 10¹⁰⁰(101-digit number)
25844727239040347180…04257632661890047999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
5.168 Γ— 10¹⁰⁰(101-digit number)
51689454478080694361…08515265323780095999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.033 Γ— 10¹⁰¹(102-digit number)
10337890895616138872…17030530647560191999
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10
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 516911

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 e09f8d2b1841f872c9d64798818dda4eb03825ae9be76b5e5bed0be93ae2a0b7

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 #516,911 on Chainz β†—
Circulating Supply:57,909,639 XPMΒ·at block #6,833,181 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