XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #509,678

Block #509,678

1CCLength 12β˜…β˜…β˜…β˜…β˜†

Cunningham Chain of the First Kind Β· Discovered 4/25/2014, 5:11:58 AM Β· Difficulty 10.8207 Β· 6,286,505 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
690f2b6d22ca5a3b069bd28f3337a5cf9f368bdeac07db8339821a7ffd4ef052
View on Chainz β†—

Height

#509,678

Difficulty

10.820713

Transactions

1

Size

208 B

Version

2

Bits

0ad21a43

Nonce

122,480,478

Timestamp

4/25/2014, 5:11:58 AM

Confirmations

6,286,505

Merkle Root

2021461d24a1fd5d06c173db4f7e2403ff6c170571da488ed7149f91146661c8
Transactions (1)
Coinbase2021461d24a1fd…149f91146661c8
1 in β†’ 1 out8.5300 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.

2.109 Γ— 10⁹⁸(99-digit number)
21096386623480578339…51619954554074082280
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
2.109 Γ— 10⁹⁸(99-digit number)
21096386623480578339…51619954554074082279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.219 Γ— 10⁹⁸(99-digit number)
42192773246961156679…03239909108148164559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
8.438 Γ— 10⁹⁸(99-digit number)
84385546493922313359…06479818216296329119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.687 Γ— 10⁹⁹(100-digit number)
16877109298784462671…12959636432592658239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.375 Γ— 10⁹⁹(100-digit number)
33754218597568925343…25919272865185316479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
6.750 Γ— 10⁹⁹(100-digit number)
67508437195137850687…51838545730370632959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.350 Γ— 10¹⁰⁰(101-digit number)
13501687439027570137…03677091460741265919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.700 Γ— 10¹⁰⁰(101-digit number)
27003374878055140275…07354182921482531839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
5.400 Γ— 10¹⁰⁰(101-digit number)
54006749756110280550…14708365842965063679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.080 Γ— 10¹⁰¹(102-digit number)
10801349951222056110…29416731685930127359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
2.160 Γ— 10¹⁰¹(102-digit number)
21602699902444112220…58833463371860254719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
12
2^11 Γ— origin βˆ’ 1
4.320 Γ— 10¹⁰¹(102-digit number)
43205399804888224440…17666926743720509439
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 12 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
ExceptionalChain length 12
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 509678

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 690f2b6d22ca5a3b069bd28f3337a5cf9f368bdeac07db8339821a7ffd4ef052

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 #509,678 on Chainz β†—
Circulating Supply:57,613,462 XPMΒ·at block #6,796,182 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