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Home/Chain Registry/Block #2,295,925

Block #2,295,925

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/14/2017, 12:13:47 PM Β· Difficulty 10.9511 Β· 4,549,768 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
83b27e621591d6eeb49d0e487871ac278ade105b35634ca0eb6c6846098c35a0
View on Chainz β†—

Difficulty

10.951084

Transactions

1

Size

200 B

Version

2

Bits

0af37a38

Nonce

1,690,118,591

Timestamp

9/14/2017, 12:13:47 PM

Confirmations

4,549,768

Merkle Root

6d043a8738d9e97099fa16af3d28f45e3c127b294b51a723450f0d3a87cc3636
Transactions (1)
Coinbase6d043a8738d9e9…0f0d3a87cc3636
1 in β†’ 1 out8.3300 XPM109 B
ARSyboNG…vbm4QQjA
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.

1.588 Γ— 10⁹⁢(97-digit number)
15880296096409892797…90409789073382195200
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
1.588 Γ— 10⁹⁢(97-digit number)
15880296096409892797…90409789073382195199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.176 Γ— 10⁹⁢(97-digit number)
31760592192819785595…80819578146764390399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
6.352 Γ— 10⁹⁢(97-digit number)
63521184385639571191…61639156293528780799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.270 Γ— 10⁹⁷(98-digit number)
12704236877127914238…23278312587057561599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.540 Γ— 10⁹⁷(98-digit number)
25408473754255828476…46556625174115123199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.081 Γ— 10⁹⁷(98-digit number)
50816947508511656953…93113250348230246399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.016 Γ— 10⁹⁸(99-digit number)
10163389501702331390…86226500696460492799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.032 Γ— 10⁹⁸(99-digit number)
20326779003404662781…72453001392920985599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.065 Γ— 10⁹⁸(99-digit number)
40653558006809325562…44906002785841971199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
8.130 Γ— 10⁹⁸(99-digit number)
81307116013618651125…89812005571683942399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.626 Γ— 10⁹⁹(100-digit number)
16261423202723730225…79624011143367884799
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11
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 2295925

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 83b27e621591d6eeb49d0e487871ac278ade105b35634ca0eb6c6846098c35a0

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 #2,295,925 on Chainz β†—
Circulating Supply:58,010,000 XPMΒ·at block #6,845,692 Β· updates every 60s
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