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Home/Chain Registry/Block #2,286,008

Block #2,286,008

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/7/2017, 6:30:31 AM Β· Difficulty 10.9555 Β· 4,547,904 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
14ad3e7c0abf52f8bab7cbfd1111bdb971426f28ccf8676519eb267caabe2b8b
View on Chainz β†—

Difficulty

10.955465

Transactions

1

Size

201 B

Version

2

Bits

0af49962

Nonce

1,028,508,137

Timestamp

9/7/2017, 6:30:31 AM

Confirmations

4,547,904

Merkle Root

7f0d80d2e0902a8a57a844b81b596e7c602a3460a20dd20360ae30ca4aaef292
Transactions (1)
Coinbase7f0d80d2e0902a…ae30ca4aaef292
1 in β†’ 1 out8.3200 XPM110 B
Ab7pf5KT…pkzYedsY
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.

8.586 Γ— 10⁹⁢(97-digit number)
85868412462416874506…36471044004577254400
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
8.586 Γ— 10⁹⁢(97-digit number)
85868412462416874506…36471044004577254401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.717 Γ— 10⁹⁷(98-digit number)
17173682492483374901…72942088009154508801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.434 Γ— 10⁹⁷(98-digit number)
34347364984966749802…45884176018309017601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.869 Γ— 10⁹⁷(98-digit number)
68694729969933499605…91768352036618035201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.373 Γ— 10⁹⁸(99-digit number)
13738945993986699921…83536704073236070401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.747 Γ— 10⁹⁸(99-digit number)
27477891987973399842…67073408146472140801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.495 Γ— 10⁹⁸(99-digit number)
54955783975946799684…34146816292944281601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.099 Γ— 10⁹⁹(100-digit number)
10991156795189359936…68293632585888563201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.198 Γ— 10⁹⁹(100-digit number)
21982313590378719873…36587265171777126401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.396 Γ— 10⁹⁹(100-digit number)
43964627180757439747…73174530343554252801
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 2286008

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 14ad3e7c0abf52f8bab7cbfd1111bdb971426f28ccf8676519eb267caabe2b8b

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 #2,286,008 on Chainz β†—
Circulating Supply:57,915,521 XPMΒ·at block #6,833,911 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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