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Home/Chain Registry/Block #494,787

Block #494,787

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 4/16/2014, 8:13:15 AM Β· Difficulty 10.7251 Β· 6,305,143 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
de585266b4ace7c39426a5cb446f4215dbbe7661e4e617ba990def3e2ab9d722
View on Chainz β†—

Height

#494,787

Difficulty

10.725118

Transactions

1

Size

207 B

Version

2

Bits

0ab9a156

Nonce

423,378,936

Timestamp

4/16/2014, 8:13:15 AM

Confirmations

6,305,143

Merkle Root

9cc2c8ee7796768a56d4719b0dde022960260359c46f5262b43b0670e1640630
Transactions (1)
Coinbase9cc2c8ee779676…3b0670e1640630
1 in β†’ 1 out8.6800 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.

1.542 Γ— 10⁹⁷(98-digit number)
15421200781188693538…28281816622694009440
Discovered Prime Numbers
p_k = 2^k Γ— origin + 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 + 1
1.542 Γ— 10⁹⁷(98-digit number)
15421200781188693538…28281816622694009441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.084 Γ— 10⁹⁷(98-digit number)
30842401562377387076…56563633245388018881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
6.168 Γ— 10⁹⁷(98-digit number)
61684803124754774152…13127266490776037761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.233 Γ— 10⁹⁸(99-digit number)
12336960624950954830…26254532981552075521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.467 Γ— 10⁹⁸(99-digit number)
24673921249901909661…52509065963104151041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.934 Γ— 10⁹⁸(99-digit number)
49347842499803819322…05018131926208302081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
9.869 Γ— 10⁹⁸(99-digit number)
98695684999607638644…10036263852416604161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.973 Γ— 10⁹⁹(100-digit number)
19739136999921527728…20072527704833208321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.947 Γ— 10⁹⁹(100-digit number)
39478273999843055457…40145055409666416641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
7.895 Γ— 10⁹⁹(100-digit number)
78956547999686110915…80290110819332833281
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 Second 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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 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 494787

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 de585266b4ace7c39426a5cb446f4215dbbe7661e4e617ba990def3e2ab9d722

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 #494,787 on Chainz β†—
Circulating Supply:57,643,499 XPMΒ·at block #6,799,929 Β· updates every 60s
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