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Home/Chain Registry/Block #2,094,632

Block #2,094,632

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 4/30/2017, 5:48:59 PM Β· Difficulty 10.8723 Β· 4,745,141 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
8d0307017fd97185c0cb78ed83a6d8b74d6b1da5a7a54b86d987b53dcc681adb
View on Chainz β†—

Difficulty

10.872308

Transactions

1

Size

201 B

Version

2

Bits

0adf4f8c

Nonce

452,915,246

Timestamp

4/30/2017, 5:48:59 PM

Confirmations

4,745,141

Merkle Root

012911a917d7b784bf640b5af7395f5f8e3af54ebe020a88cdb272d0bd10aed0
Transactions (1)
Coinbase012911a917d7b7…b272d0bd10aed0
1 in β†’ 1 out8.4500 XPM110 B
AeiKwQ7B…bY6ijdvY
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.

1.104 Γ— 10⁹⁷(98-digit number)
11041809719865986863…32678190312413470720
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
1.104 Γ— 10⁹⁷(98-digit number)
11041809719865986863…32678190312413470719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.208 Γ— 10⁹⁷(98-digit number)
22083619439731973726…65356380624826941439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.416 Γ— 10⁹⁷(98-digit number)
44167238879463947452…30712761249653882879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
8.833 Γ— 10⁹⁷(98-digit number)
88334477758927894905…61425522499307765759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.766 Γ— 10⁹⁸(99-digit number)
17666895551785578981…22851044998615531519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.533 Γ— 10⁹⁸(99-digit number)
35333791103571157962…45702089997231063039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
7.066 Γ— 10⁹⁸(99-digit number)
70667582207142315924…91404179994462126079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.413 Γ— 10⁹⁹(100-digit number)
14133516441428463184…82808359988924252159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.826 Γ— 10⁹⁹(100-digit number)
28267032882856926369…65616719977848504319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
5.653 Γ— 10⁹⁹(100-digit number)
56534065765713852739…31233439955697008639
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 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
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 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 2094632

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 8d0307017fd97185c0cb78ed83a6d8b74d6b1da5a7a54b86d987b53dcc681adb

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 #2,094,632 on Chainz β†—
Circulating Supply:57,962,474 XPMΒ·at block #6,839,772 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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