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Home/Chain Registry/Block #669,876

Block #669,876

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/9/2014, 5:02:34 AM Β· Difficulty 10.9641 Β· 6,170,312 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
c2d8d3c077d3f27e0d9d971a0d268b97586343756b30d2e10243eaec298d2ade
View on Chainz β†—

Height

#669,876

Difficulty

10.964082

Transactions

1

Size

206 B

Version

2

Bits

0af6ce13

Nonce

501,010,380

Timestamp

8/9/2014, 5:02:34 AM

Confirmations

6,170,312

Merkle Root

5c43e8aabd680c9aaf5efe889f05003bb7a2684a76450cb20a170862056c0f86
Transactions (1)
Coinbase5c43e8aabd680c…170862056c0f86
1 in β†’ 1 out8.3100 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.

5.970 Γ— 10⁹⁡(96-digit number)
59705450790241431536…36113327083786095200
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
5.970 Γ— 10⁹⁡(96-digit number)
59705450790241431536…36113327083786095201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.194 Γ— 10⁹⁢(97-digit number)
11941090158048286307…72226654167572190401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.388 Γ— 10⁹⁢(97-digit number)
23882180316096572614…44453308335144380801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.776 Γ— 10⁹⁢(97-digit number)
47764360632193145229…88906616670288761601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
9.552 Γ— 10⁹⁢(97-digit number)
95528721264386290458…77813233340577523201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.910 Γ— 10⁹⁷(98-digit number)
19105744252877258091…55626466681155046401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.821 Γ— 10⁹⁷(98-digit number)
38211488505754516183…11252933362310092801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
7.642 Γ— 10⁹⁷(98-digit number)
76422977011509032366…22505866724620185601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.528 Γ— 10⁹⁸(99-digit number)
15284595402301806473…45011733449240371201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.056 Γ— 10⁹⁸(99-digit number)
30569190804603612946…90023466898480742401
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 669876

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 c2d8d3c077d3f27e0d9d971a0d268b97586343756b30d2e10243eaec298d2ade

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 #669,876 on Chainz β†—
Circulating Supply:57,965,828 XPMΒ·at block #6,840,187 Β· updates every 60s
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