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Block #509,037

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 4/24/2014, 6:57:15 PM Β· Difficulty 10.8198 Β· 6,296,375 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
dcf38df25864a3bf807409122dfd90210d6f12e2368a6f02a2623e0209318668
View on Chainz β†—

Height

#509,037

Difficulty

10.819774

Transactions

1

Size

207 B

Version

2

Bits

0ad1dcba

Nonce

754,148,064

Timestamp

4/24/2014, 6:57:15 PM

Confirmations

6,296,375

Merkle Root

edaed0c9c763c2cbec9955132da8a07181e90b23159231cdde60b560afc2bc89
Transactions (1)
Coinbaseedaed0c9c763c2…60b560afc2bc89
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.

5.924 Γ— 10⁹⁷(98-digit number)
59241112827994853331…15230406881131403760
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
5.924 Γ— 10⁹⁷(98-digit number)
59241112827994853331…15230406881131403759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.184 Γ— 10⁹⁸(99-digit number)
11848222565598970666…30460813762262807519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.369 Γ— 10⁹⁸(99-digit number)
23696445131197941332…60921627524525615039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.739 Γ— 10⁹⁸(99-digit number)
47392890262395882665…21843255049051230079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
9.478 Γ— 10⁹⁸(99-digit number)
94785780524791765330…43686510098102460159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.895 Γ— 10⁹⁹(100-digit number)
18957156104958353066…87373020196204920319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.791 Γ— 10⁹⁹(100-digit number)
37914312209916706132…74746040392409840639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
7.582 Γ— 10⁹⁹(100-digit number)
75828624419833412264…49492080784819681279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.516 Γ— 10¹⁰⁰(101-digit number)
15165724883966682452…98984161569639362559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.033 Γ— 10¹⁰⁰(101-digit number)
30331449767933364905…97968323139278725119
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 509037

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 dcf38df25864a3bf807409122dfd90210d6f12e2368a6f02a2623e0209318668

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 #509,037 on Chainz β†—
Circulating Supply:57,687,366 XPMΒ·at block #6,805,411 Β· updates every 60s
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