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Home/Chain Registry/Block #666,932

Block #666,932

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/7/2014, 8:56:25 AM Β· Difficulty 10.9618 Β· 6,160,103 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
33faa923d5a7bdbcdea0cce2a723d00ef448fff76a1b8ec5ae99704c1ea7edd9
View on Chainz β†—

Height

#666,932

Difficulty

10.961816

Transactions

3

Size

957 B

Version

2

Bits

0af63994

Nonce

317,959,746

Timestamp

8/7/2014, 8:56:25 AM

Confirmations

6,160,103

Merkle Root

03132e51ca5ae0c89aa8c5319ee4ee49c57de1044401bea59900939d89d58998
Transactions (3)
Coinbase08007682e5bf32…10484d90446fb4
1 in β†’ 1 out8.3300 XPM116 B
ANSXnLY2…Sd25TjkD
dbd13d05830797…7c0a34ae6daf41
3 in β†’ 2 out23.9300 XPM523 B
AKQb78kd…kP7kYNJqAPrPf4P5…k76UXoEi
30c4570a80c84d…47ebebb4f9e0ad
1 in β†’ 2 out0.6751 XPM227 B
Ae7ht6Sj…7i8cq412ANMhgngM…EVMj7xoE
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.

2.144 Γ— 10⁹⁢(97-digit number)
21442976027707963394…06987751175407206400
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
2.144 Γ— 10⁹⁢(97-digit number)
21442976027707963394…06987751175407206401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.288 Γ— 10⁹⁢(97-digit number)
42885952055415926788…13975502350814412801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
8.577 Γ— 10⁹⁢(97-digit number)
85771904110831853577…27951004701628825601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.715 Γ— 10⁹⁷(98-digit number)
17154380822166370715…55902009403257651201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.430 Γ— 10⁹⁷(98-digit number)
34308761644332741431…11804018806515302401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.861 Γ— 10⁹⁷(98-digit number)
68617523288665482862…23608037613030604801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.372 Γ— 10⁹⁸(99-digit number)
13723504657733096572…47216075226061209601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.744 Γ— 10⁹⁸(99-digit number)
27447009315466193144…94432150452122419201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.489 Γ— 10⁹⁸(99-digit number)
54894018630932386289…88864300904244838401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.097 Γ— 10⁹⁹(100-digit number)
10978803726186477257…77728601808489676801
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 666932

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 33faa923d5a7bdbcdea0cce2a723d00ef448fff76a1b8ec5ae99704c1ea7edd9

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 #666,932 on Chainz β†—
Circulating Supply:57,860,459 XPMΒ·at block #6,827,034 Β· updates every 60s
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