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Home/Chain Registry/Block #2,856,823

Block #2,856,823

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/27/2018, 7:11:31 AM Β· Difficulty 11.6904 Β· 3,975,803 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
30f32ed0e6e5e8d89e992700d23df9c0efc2b84bfec0e20aee442950b951794a
View on Chainz β†—

Difficulty

11.690365

Transactions

1

Size

201 B

Version

2

Bits

0bb0bbbc

Nonce

1,058,557,805

Timestamp

9/27/2018, 7:11:31 AM

Confirmations

3,975,803

Merkle Root

c9e0b00e4567d7070a1a17d6b62b4aa82e6d09f6c5f57d2bd6d4ea0bd34459c9
Transactions (1)
Coinbasec9e0b00e4567d7…d4ea0bd34459c9
1 in β†’ 1 out7.3000 XPM110 B
AUMQRepm…tAfKmdW1
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.

7.031 Γ— 10⁹⁷(98-digit number)
70312004015868145551…98485843093975936000
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
7.031 Γ— 10⁹⁷(98-digit number)
70312004015868145551…98485843093975936001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.406 Γ— 10⁹⁸(99-digit number)
14062400803173629110…96971686187951872001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.812 Γ— 10⁹⁸(99-digit number)
28124801606347258220…93943372375903744001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.624 Γ— 10⁹⁸(99-digit number)
56249603212694516440…87886744751807488001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.124 Γ— 10⁹⁹(100-digit number)
11249920642538903288…75773489503614976001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.249 Γ— 10⁹⁹(100-digit number)
22499841285077806576…51546979007229952001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.499 Γ— 10⁹⁹(100-digit number)
44999682570155613152…03093958014459904001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
8.999 Γ— 10⁹⁹(100-digit number)
89999365140311226305…06187916028919808001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.799 Γ— 10¹⁰⁰(101-digit number)
17999873028062245261…12375832057839616001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.599 Γ— 10¹⁰⁰(101-digit number)
35999746056124490522…24751664115679232001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
7.199 Γ— 10¹⁰⁰(101-digit number)
71999492112248981044…49503328231358464001
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 2856823

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 30f32ed0e6e5e8d89e992700d23df9c0efc2b84bfec0e20aee442950b951794a

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 #2,856,823 on Chainz β†—
Circulating Supply:57,905,156 XPMΒ·at block #6,832,625 Β· updates every 60s
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