XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #503,595

Block #503,595

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 4/21/2014, 5:02:50 AM Β· Difficulty 10.8087 Β· 6,297,131 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
dd8f96873f5ae9a1d518768daa0aa1fe800322575b490c4c112e31f919665243
View on Chainz β†—

Height

#503,595

Difficulty

10.808658

Transactions

1

Size

208 B

Version

2

Bits

0acf043d

Nonce

20,877,285

Timestamp

4/21/2014, 5:02:50 AM

Confirmations

6,297,131

Merkle Root

bcae4b26eacf90b338e9912660c20c0abdae90bb529df77ea892f75de4ef5f9f
Transactions (1)
Coinbasebcae4b26eacf90…92f75de4ef5f9f
1 in β†’ 1 out8.5500 XPM116 B
AbwWkWZt…kawDhufa
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.

5.593 Γ— 10⁹⁸(99-digit number)
55932704496027848777…83131728629480819840
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
5.593 Γ— 10⁹⁸(99-digit number)
55932704496027848777…83131728629480819839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.118 Γ— 10⁹⁹(100-digit number)
11186540899205569755…66263457258961639679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.237 Γ— 10⁹⁹(100-digit number)
22373081798411139510…32526914517923279359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.474 Γ— 10⁹⁹(100-digit number)
44746163596822279021…65053829035846558719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
8.949 Γ— 10⁹⁹(100-digit number)
89492327193644558043…30107658071693117439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.789 Γ— 10¹⁰⁰(101-digit number)
17898465438728911608…60215316143386234879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.579 Γ— 10¹⁰⁰(101-digit number)
35796930877457823217…20430632286772469759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
7.159 Γ— 10¹⁰⁰(101-digit number)
71593861754915646434…40861264573544939519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.431 Γ— 10¹⁰¹(102-digit number)
14318772350983129286…81722529147089879039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.863 Γ— 10¹⁰¹(102-digit number)
28637544701966258573…63445058294179758079
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 503595

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 dd8f96873f5ae9a1d518768daa0aa1fe800322575b490c4c112e31f919665243

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 #503,595 on Chainz β†—
Circulating Supply:57,649,877 XPMΒ·at block #6,800,725 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.
AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK