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Block #806,412

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/11/2014, 9:07:10 AM Β· Difficulty 10.9742 Β· 6,006,543 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
48127bfe26b3b44f550c8efb70731225fb2b96a448919b5cd79d4c302da0d649
View on Chainz β†—

Height

#806,412

Difficulty

10.974242

Transactions

1

Size

208 B

Version

2

Bits

0af967e7

Nonce

258,649,296

Timestamp

11/11/2014, 9:07:10 AM

Confirmations

6,006,543

Merkle Root

21b75a42a65368ce8aae5bc79a5b3568f1ebeacf192ed8cef533648200133487
Transactions (1)
Coinbase21b75a42a65368…33648200133487
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.

2.472 Γ— 10⁹⁸(99-digit number)
24720945681927270417…75299462864350658560
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
2.472 Γ— 10⁹⁸(99-digit number)
24720945681927270417…75299462864350658561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.944 Γ— 10⁹⁸(99-digit number)
49441891363854540834…50598925728701317121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
9.888 Γ— 10⁹⁸(99-digit number)
98883782727709081669…01197851457402634241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.977 Γ— 10⁹⁹(100-digit number)
19776756545541816333…02395702914805268481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.955 Γ— 10⁹⁹(100-digit number)
39553513091083632667…04791405829610536961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
7.910 Γ— 10⁹⁹(100-digit number)
79107026182167265335…09582811659221073921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.582 Γ— 10¹⁰⁰(101-digit number)
15821405236433453067…19165623318442147841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.164 Γ— 10¹⁰⁰(101-digit number)
31642810472866906134…38331246636884295681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
6.328 Γ— 10¹⁰⁰(101-digit number)
63285620945733812268…76662493273768591361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.265 Γ— 10¹⁰¹(102-digit number)
12657124189146762453…53324986547537182721
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 806412

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 48127bfe26b3b44f550c8efb70731225fb2b96a448919b5cd79d4c302da0d649

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 #806,412 on Chainz β†—
Circulating Supply:57,747,681 XPMΒ·at block #6,812,954 Β· updates every 60s
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