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Home/Chain Registry/Block #2,284,220

Block #2,284,220

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/6/2017, 1:22:27 AM Β· Difficulty 10.9551 Β· 4,533,828 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
3d22fc12e587bb25d96cfd30e925d8f59efc84860e8567d186f7aafcea31ae1a
View on Chainz β†—

Difficulty

10.955054

Transactions

1

Size

200 B

Version

2

Bits

0af47e6d

Nonce

1,250,470,788

Timestamp

9/6/2017, 1:22:27 AM

Confirmations

4,533,828

Merkle Root

b8791267a8c8521f73e103457d7f28cb4f37748482725c60e58ef29d3e8f13de
Transactions (1)
Coinbaseb8791267a8c852…8ef29d3e8f13de
1 in β†’ 1 out8.3200 XPM110 B
AbZLw7DP…bx619oSy
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.

4.012 Γ— 10⁹⁡(96-digit number)
40128814514448674158…25276954279626311280
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
4.012 Γ— 10⁹⁡(96-digit number)
40128814514448674158…25276954279626311281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
8.025 Γ— 10⁹⁡(96-digit number)
80257629028897348317…50553908559252622561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.605 Γ— 10⁹⁢(97-digit number)
16051525805779469663…01107817118505245121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.210 Γ— 10⁹⁢(97-digit number)
32103051611558939327…02215634237010490241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
6.420 Γ— 10⁹⁢(97-digit number)
64206103223117878654…04431268474020980481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.284 Γ— 10⁹⁷(98-digit number)
12841220644623575730…08862536948041960961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.568 Γ— 10⁹⁷(98-digit number)
25682441289247151461…17725073896083921921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
5.136 Γ— 10⁹⁷(98-digit number)
51364882578494302923…35450147792167843841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.027 Γ— 10⁹⁸(99-digit number)
10272976515698860584…70900295584335687681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.054 Γ— 10⁹⁸(99-digit number)
20545953031397721169…41800591168671375361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
4.109 Γ— 10⁹⁸(99-digit number)
41091906062795442338…83601182337342750721
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 2284220

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 3d22fc12e587bb25d96cfd30e925d8f59efc84860e8567d186f7aafcea31ae1a

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 #2,284,220 on Chainz β†—
Circulating Supply:57,788,455 XPMΒ·at block #6,818,047 Β· updates every 60s
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