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Home/Chain Registry/Block #3,071,093

Block #3,071,093

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 2/27/2019, 3:57:29 PM Β· Difficulty 10.9961 Β· 3,772,676 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
39c003784eb1c4694f1dde5ff66b5cced5dcca6d0537f8ede91f7d273268e2da
View on Chainz β†—

Difficulty

10.996075

Transactions

1

Size

200 B

Version

2

Bits

0afefec0

Nonce

321,166,570

Timestamp

2/27/2019, 3:57:29 PM

Confirmations

3,772,676

Merkle Root

7f13141f48c8f2d5b41c34b5619c7cdf5121ab2b1571fe51723e77de458fdef9
Transactions (1)
Coinbase7f13141f48c8f2…3e77de458fdef9
1 in β†’ 1 out8.2600 XPM110 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.

3.669 Γ— 10⁹⁡(96-digit number)
36691702594085159560…94544248900485734400
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
3.669 Γ— 10⁹⁡(96-digit number)
36691702594085159560…94544248900485734401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
7.338 Γ— 10⁹⁡(96-digit number)
73383405188170319120…89088497800971468801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.467 Γ— 10⁹⁢(97-digit number)
14676681037634063824…78176995601942937601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.935 Γ— 10⁹⁢(97-digit number)
29353362075268127648…56353991203885875201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
5.870 Γ— 10⁹⁢(97-digit number)
58706724150536255296…12707982407771750401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.174 Γ— 10⁹⁷(98-digit number)
11741344830107251059…25415964815543500801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.348 Γ— 10⁹⁷(98-digit number)
23482689660214502118…50831929631087001601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.696 Γ— 10⁹⁷(98-digit number)
46965379320429004236…01663859262174003201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
9.393 Γ— 10⁹⁷(98-digit number)
93930758640858008473…03327718524348006401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.878 Γ— 10⁹⁸(99-digit number)
18786151728171601694…06655437048696012801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
3.757 Γ— 10⁹⁸(99-digit number)
37572303456343203389…13310874097392025601
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 3071093

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 39c003784eb1c4694f1dde5ff66b5cced5dcca6d0537f8ede91f7d273268e2da

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 #3,071,093 on Chainz β†—
Circulating Supply:57,994,526 XPMΒ·at block #6,843,768 Β· updates every 60s
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