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Home/Chain Registry/Block #2,069,416

Block #2,069,416

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 4/13/2017, 2:29:11 PM Β· Difficulty 10.8571 Β· 4,772,738 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
2a0e1df2276e607c72401d12ef4a546019bb7dbc0cbcbb4d7fa4d7fa1bc0b0d5
View on Chainz β†—

Difficulty

10.857148

Transactions

1

Size

199 B

Version

2

Bits

0adb6e0c

Nonce

413,318,476

Timestamp

4/13/2017, 2:29:11 PM

Confirmations

4,772,738

Merkle Root

55d5a86532093e39f266ba5748e9e3a83b983a00a61157f35042220daa748b01
Transactions (1)
Coinbase55d5a86532093e…42220daa748b01
1 in β†’ 1 out8.4700 XPM109 B
AGfA5stS…79Cs63aa
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.

8.514 Γ— 10⁹³(94-digit number)
85143469016094541489…94656338691020762500
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
8.514 Γ— 10⁹³(94-digit number)
85143469016094541489…94656338691020762501
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.702 Γ— 10⁹⁴(95-digit number)
17028693803218908297…89312677382041525001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.405 Γ— 10⁹⁴(95-digit number)
34057387606437816595…78625354764083050001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.811 Γ— 10⁹⁴(95-digit number)
68114775212875633191…57250709528166100001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.362 Γ— 10⁹⁡(96-digit number)
13622955042575126638…14501419056332200001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.724 Γ— 10⁹⁡(96-digit number)
27245910085150253276…29002838112664400001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.449 Γ— 10⁹⁡(96-digit number)
54491820170300506553…58005676225328800001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.089 Γ— 10⁹⁢(97-digit number)
10898364034060101310…16011352450657600001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.179 Γ— 10⁹⁢(97-digit number)
21796728068120202621…32022704901315200001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.359 Γ— 10⁹⁢(97-digit number)
43593456136240405242…64045409802630400001
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 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
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 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 2069416

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 2a0e1df2276e607c72401d12ef4a546019bb7dbc0cbcbb4d7fa4d7fa1bc0b0d5

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 #2,069,416 on Chainz β†—
Circulating Supply:57,981,622 XPMΒ·at block #6,842,153 Β· updates every 60s
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