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Block #499,354

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 4/18/2014, 1:58:24 PM Β· Difficulty 10.7899 Β· 6,317,440 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
4157ba3e9d94aa81d61bedcd48b49bfa04fa8569f22e8a5bd5c589ed5900ee23
View on Chainz β†—

Height

#499,354

Difficulty

10.789852

Transactions

1

Size

207 B

Version

2

Bits

0aca33c4

Nonce

372,203,454

Timestamp

4/18/2014, 1:58:24 PM

Confirmations

6,317,440

Merkle Root

34a18300233b6467fce36d1359143762d506c1b21ad9b6d1caf9a869976ecefb
Transactions (1)
Coinbase34a18300233b64…f9a869976ecefb
1 in β†’ 1 out8.5800 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.

6.833 Γ— 10⁹⁷(98-digit number)
68330862782818605209…77027559771955338960
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
6.833 Γ— 10⁹⁷(98-digit number)
68330862782818605209…77027559771955338959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.366 Γ— 10⁹⁸(99-digit number)
13666172556563721041…54055119543910677919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.733 Γ— 10⁹⁸(99-digit number)
27332345113127442083…08110239087821355839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.466 Γ— 10⁹⁸(99-digit number)
54664690226254884167…16220478175642711679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.093 Γ— 10⁹⁹(100-digit number)
10932938045250976833…32440956351285423359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.186 Γ— 10⁹⁹(100-digit number)
21865876090501953667…64881912702570846719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.373 Γ— 10⁹⁹(100-digit number)
43731752181003907334…29763825405141693439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
8.746 Γ— 10⁹⁹(100-digit number)
87463504362007814668…59527650810283386879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.749 Γ— 10¹⁰⁰(101-digit number)
17492700872401562933…19055301620566773759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.498 Γ— 10¹⁰⁰(101-digit number)
34985401744803125867…38110603241133547519
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 499354

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 4157ba3e9d94aa81d61bedcd48b49bfa04fa8569f22e8a5bd5c589ed5900ee23

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 #499,354 on Chainz β†—
Circulating Supply:57,778,388 XPMΒ·at block #6,816,793 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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