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Home/Chain Registry/Block #3,412,387

Block #3,412,387

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 10/30/2019, 5:26:52 AM Β· Difficulty 10.9850 Β· 3,414,736 confirmations

TWN
Bi-Twin Chain

Interleaved pairs of primes that differ by 2, forming twin prime pairs at each level.

Block Header
Block Hash
e1f7241b5e4ca753eae66164c16dd007749847cff73ba93ad5ba2c6e2fc1f7f8
View on Chainz β†—

Difficulty

10.984952

Transactions

1

Size

200 B

Version

2

Bits

0afc25c9

Nonce

289,682,868

Timestamp

10/30/2019, 5:26:52 AM

Confirmations

3,414,736

Merkle Root

19d6c4ee2103ad7ecee97275fd37eddc05ed03319f6d44ba3978f88a508fc0e1
Transactions (1)
Coinbase19d6c4ee2103ad…78f88a508fc0e1
1 in β†’ 1 out8.2700 XPM110 B
ASiq2qtK…VMhmk7yL
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.

1.292 Γ— 10⁹⁴(95-digit number)
12926870698391204035…85401773959568709120
Discovered Prime Numbers
Lower: 2^k Γ— origin βˆ’ 1 | Upper: 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.

Level 0 β€” Twin Prime Pair (origin Β± 1)
origin βˆ’ 1
1.292 Γ— 10⁹⁴(95-digit number)
12926870698391204035…85401773959568709119
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.292 Γ— 10⁹⁴(95-digit number)
12926870698391204035…85401773959568709121
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: origin + 1 βˆ’ origin βˆ’ 1 = 2 (twin primes βœ“)
Level 1 β€” Twin Prime Pair (2^1 Γ— origin Β± 1)
2^1 Γ— origin βˆ’ 1
2.585 Γ— 10⁹⁴(95-digit number)
25853741396782408070…70803547919137418239
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.585 Γ— 10⁹⁴(95-digit number)
25853741396782408070…70803547919137418241
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^1 Γ— origin + 1 βˆ’ 2^1 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 2 β€” Twin Prime Pair (2^2 Γ— origin Β± 1)
2^2 Γ— origin βˆ’ 1
5.170 Γ— 10⁹⁴(95-digit number)
51707482793564816141…41607095838274836479
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.170 Γ— 10⁹⁴(95-digit number)
51707482793564816141…41607095838274836481
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^2 Γ— origin + 1 βˆ’ 2^2 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 3 β€” Twin Prime Pair (2^3 Γ— origin Β± 1)
2^3 Γ— origin βˆ’ 1
1.034 Γ— 10⁹⁡(96-digit number)
10341496558712963228…83214191676549672959
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.034 Γ— 10⁹⁡(96-digit number)
10341496558712963228…83214191676549672961
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 4 β€” Twin Prime Pair (2^4 Γ— origin Β± 1)
2^4 Γ— origin βˆ’ 1
2.068 Γ— 10⁹⁡(96-digit number)
20682993117425926456…66428383353099345919
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.068 Γ— 10⁹⁡(96-digit number)
20682993117425926456…66428383353099345921
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 10 consecutive prime numbers forming a Bi-Twin Chain. 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 TWN formula:

TWN: twin pairs (p, p+2) where p = origin/primorial βˆ’ 1 and p+2 = origin/primorial + 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 3412387

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 e1f7241b5e4ca753eae66164c16dd007749847cff73ba93ad5ba2c6e2fc1f7f8

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 #3,412,387 on Chainz β†—
Circulating Supply:57,861,165 XPMΒ·at block #6,827,122 Β· updates every 60s
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