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Home/Chain Registry/Block #2,284,637

Block #2,284,637

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/6/2017, 8:11:57 AM Β· Difficulty 10.9551 Β· 4,556,696 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
2762fc763059f641e01eccb6c630494e9b236cb564539b9ad22089ba045cd893
View on Chainz β†—

Difficulty

10.955137

Transactions

1

Size

200 B

Version

2

Bits

0af483dd

Nonce

208,068,693

Timestamp

9/6/2017, 8:11:57 AM

Confirmations

4,556,696

Merkle Root

0b711281c53662d27a109f14ed9be948518ec87fc2ad4c7f119b36772f4a6ecd
Transactions (1)
Coinbase0b711281c53662…9b36772f4a6ecd
1 in β†’ 1 out8.3200 XPM109 B
AKVxuAwu…vWfuPeo5
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.

1.452 Γ— 10⁹⁢(97-digit number)
14527597293180911256…62868637341590097920
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
1.452 Γ— 10⁹⁢(97-digit number)
14527597293180911256…62868637341590097921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.905 Γ— 10⁹⁢(97-digit number)
29055194586361822512…25737274683180195841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
5.811 Γ— 10⁹⁢(97-digit number)
58110389172723645025…51474549366360391681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.162 Γ— 10⁹⁷(98-digit number)
11622077834544729005…02949098732720783361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.324 Γ— 10⁹⁷(98-digit number)
23244155669089458010…05898197465441566721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.648 Γ— 10⁹⁷(98-digit number)
46488311338178916020…11796394930883133441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
9.297 Γ— 10⁹⁷(98-digit number)
92976622676357832040…23592789861766266881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.859 Γ— 10⁹⁸(99-digit number)
18595324535271566408…47185579723532533761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.719 Γ— 10⁹⁸(99-digit number)
37190649070543132816…94371159447065067521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
7.438 Γ— 10⁹⁸(99-digit number)
74381298141086265632…88742318894130135041
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 2284637

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 2762fc763059f641e01eccb6c630494e9b236cb564539b9ad22089ba045cd893

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 #2,284,637 on Chainz β†—
Circulating Supply:57,975,028 XPMΒ·at block #6,841,332 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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