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Home/Chain Registry/Block #3,050,710

Block #3,050,710

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 2/13/2019, 5:48:06 AM Β· Difficulty 10.9961 Β· 3,790,209 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
c4d0625b1fd8ed3d07bfb30a382b4ce05dd95f65c558bbca490765a1208952e0
View on Chainz β†—

Difficulty

10.996061

Transactions

1

Size

198 B

Version

2

Bits

0afefdda

Nonce

377,802,035

Timestamp

2/13/2019, 5:48:06 AM

Confirmations

3,790,209

Merkle Root

453674770abe40e96f0f3cdf145f5fe33ec9b50681d793ddffab98fba691e852
Transactions (1)
Coinbase453674770abe40…ab98fba691e852
1 in β†’ 1 out8.2600 XPM109 B
AbXwmGxD…4XXYP765
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.

2.419 Γ— 10⁹³(94-digit number)
24194927394447124318…42522441057962322480
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
2.419 Γ— 10⁹³(94-digit number)
24194927394447124318…42522441057962322481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.838 Γ— 10⁹³(94-digit number)
48389854788894248637…85044882115924644961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
9.677 Γ— 10⁹³(94-digit number)
96779709577788497275…70089764231849289921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.935 Γ— 10⁹⁴(95-digit number)
19355941915557699455…40179528463698579841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.871 Γ— 10⁹⁴(95-digit number)
38711883831115398910…80359056927397159681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
7.742 Γ— 10⁹⁴(95-digit number)
77423767662230797820…60718113854794319361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.548 Γ— 10⁹⁡(96-digit number)
15484753532446159564…21436227709588638721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.096 Γ— 10⁹⁡(96-digit number)
30969507064892319128…42872455419177277441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
6.193 Γ— 10⁹⁡(96-digit number)
61939014129784638256…85744910838354554881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.238 Γ— 10⁹⁢(97-digit number)
12387802825956927651…71489821676709109761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
2.477 Γ— 10⁹⁢(97-digit number)
24775605651913855302…42979643353418219521
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 3050710

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 c4d0625b1fd8ed3d07bfb30a382b4ce05dd95f65c558bbca490765a1208952e0

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 #3,050,710 on Chainz β†—
Circulating Supply:57,971,703 XPMΒ·at block #6,840,918 Β· updates every 60s
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