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Home/Chain Registry/Block #2,825,871

Block #2,825,871

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/5/2018, 1:26:09 PM Β· Difficulty 11.7102 Β· 4,015,873 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
ac9629280f75ccb9e79a8f6c94087d4dddb54f9f150db436fed9a9e11446b963
View on Chainz β†—

Difficulty

11.710231

Transactions

1

Size

201 B

Version

2

Bits

0bb5d1ad

Nonce

1,950,027,932

Timestamp

9/5/2018, 1:26:09 PM

Confirmations

4,015,873

Merkle Root

ef7e4b6e2ff3b2a12e1eecdc55f429743d9fd7013698eb81414aff8f8b01dbc8
Transactions (1)
Coinbaseef7e4b6e2ff3b2…4aff8f8b01dbc8
1 in β†’ 1 out7.2800 XPM110 B
AMup1Caf…zBdXXWjL
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.

4.290 Γ— 10⁹⁷(98-digit number)
42904000299532130658…14257248614580817920
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
4.290 Γ— 10⁹⁷(98-digit number)
42904000299532130658…14257248614580817921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
8.580 Γ— 10⁹⁷(98-digit number)
85808000599064261317…28514497229161635841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.716 Γ— 10⁹⁸(99-digit number)
17161600119812852263…57028994458323271681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.432 Γ— 10⁹⁸(99-digit number)
34323200239625704526…14057988916646543361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
6.864 Γ— 10⁹⁸(99-digit number)
68646400479251409053…28115977833293086721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.372 Γ— 10⁹⁹(100-digit number)
13729280095850281810…56231955666586173441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.745 Γ— 10⁹⁹(100-digit number)
27458560191700563621…12463911333172346881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
5.491 Γ— 10⁹⁹(100-digit number)
54917120383401127242…24927822666344693761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.098 Γ— 10¹⁰⁰(101-digit number)
10983424076680225448…49855645332689387521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.196 Γ— 10¹⁰⁰(101-digit number)
21966848153360450897…99711290665378775041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
4.393 Γ— 10¹⁰⁰(101-digit number)
43933696306720901794…99422581330757550081
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 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
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 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 2825871

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 ac9629280f75ccb9e79a8f6c94087d4dddb54f9f150db436fed9a9e11446b963

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 #2,825,871 on Chainz β†—
Circulating Supply:57,978,336 XPMΒ·at block #6,841,743 Β· updates every 60s
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