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Block #818,591

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/19/2014, 2:29:45 PM Β· Difficulty 10.9763 Β· 5,982,046 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
d6606f1ba42a37a0bd5ff87b368f17e135aa6b285c8f48b548b8db94e035c55d
View on Chainz β†—

Height

#818,591

Difficulty

10.976267

Transactions

1

Size

206 B

Version

2

Bits

0af9ec9a

Nonce

294,636,575

Timestamp

11/19/2014, 2:29:45 PM

Confirmations

5,982,046

Merkle Root

9b40246f4360e4d7f7e5ab99be2abcb926e1c2821f658a70048c4915fbce6669
Transactions (1)
Coinbase9b40246f4360e4…8c4915fbce6669
1 in β†’ 1 out8.2900 XPM116 B
ANSXnLY2…Sd25TjkD
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.

3.056 Γ— 10⁹⁡(96-digit number)
30560698610584405537…45958280720626541500
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
3.056 Γ— 10⁹⁡(96-digit number)
30560698610584405537…45958280720626541501
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
6.112 Γ— 10⁹⁡(96-digit number)
61121397221168811075…91916561441253083001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.222 Γ— 10⁹⁢(97-digit number)
12224279444233762215…83833122882506166001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.444 Γ— 10⁹⁢(97-digit number)
24448558888467524430…67666245765012332001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.889 Γ— 10⁹⁢(97-digit number)
48897117776935048860…35332491530024664001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
9.779 Γ— 10⁹⁢(97-digit number)
97794235553870097720…70664983060049328001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.955 Γ— 10⁹⁷(98-digit number)
19558847110774019544…41329966120098656001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.911 Γ— 10⁹⁷(98-digit number)
39117694221548039088…82659932240197312001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
7.823 Γ— 10⁹⁷(98-digit number)
78235388443096078176…65319864480394624001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.564 Γ— 10⁹⁸(99-digit number)
15647077688619215635…30639728960789248001
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 818591

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 d6606f1ba42a37a0bd5ff87b368f17e135aa6b285c8f48b548b8db94e035c55d

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 #818,591 on Chainz β†—
Circulating Supply:57,649,161 XPMΒ·at block #6,800,636 Β· updates every 60s
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