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Block #7,996

1CCLength 7β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/10/2013, 1:30:00 PM Β· Difficulty 7.5462 Β· 6,793,616 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
49b76fe31bf9ea9b74dec8713f382c65a8b34546f6b898b3aeb4aabc2a19ff4f
View on Chainz β†—

Height

#7,996

Difficulty

7.546169

Transactions

1

Size

199 B

Version

2

Bits

078bd1c3

Nonce

27

Timestamp

7/10/2013, 1:30:00 PM

Confirmations

6,793,616

Merkle Root

96f6ce029adbbf7cb6a719bb3b0dc8d96d405268d21703c5221d6fa7f951cd19
Transactions (1)
Coinbase96f6ce029adbbf…1d6fa7f951cd19
1 in β†’ 1 out17.5400 XPM108 B
ANy4knks…wNEWCdkj
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.

5.382 Γ— 10⁹⁢(97-digit number)
53823816744997030959…56416262199496819710
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
5.382 Γ— 10⁹⁢(97-digit number)
53823816744997030959…56416262199496819709
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.076 Γ— 10⁹⁷(98-digit number)
10764763348999406191…12832524398993639419
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.152 Γ— 10⁹⁷(98-digit number)
21529526697998812383…25665048797987278839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.305 Γ— 10⁹⁷(98-digit number)
43059053395997624767…51330097595974557679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
8.611 Γ— 10⁹⁷(98-digit number)
86118106791995249535…02660195191949115359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.722 Γ— 10⁹⁸(99-digit number)
17223621358399049907…05320390383898230719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.444 Γ— 10⁹⁸(99-digit number)
34447242716798099814…10640780767796461439
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 7 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
CommonChain length 7
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 7996

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 49b76fe31bf9ea9b74dec8713f382c65a8b34546f6b898b3aeb4aabc2a19ff4f

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 #7,996 on Chainz β†—
Circulating Supply:57,656,978 XPMΒ·at block #6,801,611 Β· updates every 60s
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