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Block #494,686

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 4/16/2014, 7:01:47 AM Β· Difficulty 10.7236 Β· 6,317,880 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
0b676eb8e396df64fea47ea759201fceeb728020fd0e4b11a25100b1f59070d6
View on Chainz β†—

Height

#494,686

Difficulty

10.723559

Transactions

1

Size

208 B

Version

2

Bits

0ab93b2e

Nonce

355,154

Timestamp

4/16/2014, 7:01:47 AM

Confirmations

6,317,880

Merkle Root

26f00f618e0c08c11f8922cbd70ee93bd144e6546de3c7577a3112fdc7416c05
Transactions (1)
Coinbase26f00f618e0c08…3112fdc7416c05
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.

1.356 Γ— 10⁹⁹(100-digit number)
13560277659854905024…00068169221171822200
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
1.356 Γ— 10⁹⁹(100-digit number)
13560277659854905024…00068169221171822199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.712 Γ— 10⁹⁹(100-digit number)
27120555319709810049…00136338442343644399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.424 Γ— 10⁹⁹(100-digit number)
54241110639419620099…00272676884687288799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.084 Γ— 10¹⁰⁰(101-digit number)
10848222127883924019…00545353769374577599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.169 Γ— 10¹⁰⁰(101-digit number)
21696444255767848039…01090707538749155199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.339 Γ— 10¹⁰⁰(101-digit number)
43392888511535696079…02181415077498310399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
8.678 Γ— 10¹⁰⁰(101-digit number)
86785777023071392158…04362830154996620799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.735 Γ— 10¹⁰¹(102-digit number)
17357155404614278431…08725660309993241599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.471 Γ— 10¹⁰¹(102-digit number)
34714310809228556863…17451320619986483199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
6.942 Γ— 10¹⁰¹(102-digit number)
69428621618457113727…34902641239972966399
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 494686

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 0b676eb8e396df64fea47ea759201fceeb728020fd0e4b11a25100b1f59070d6

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 #494,686 on Chainz β†—
Circulating Supply:57,744,560 XPMΒ·at block #6,812,565 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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