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Block #3,372,456

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 9/28/2019, 7:33:00 AM Β· Difficulty 10.9948 Β· 3,464,215 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
e9238d9e0c61ddf23ea7b57732a0f23c75a1f10df9834c8cf9b6c3c3038043c2
View on Chainz β†—

Difficulty

10.994814

Transactions

1

Size

201 B

Version

2

Bits

0afeac1f

Nonce

1,442,691,429

Timestamp

9/28/2019, 7:33:00 AM

Confirmations

3,464,215

Merkle Root

b5bd5c475aa0e4ff0f630d8202dc7707855203c7d09f8019b0a7edda958d4136
Transactions (1)
Coinbaseb5bd5c475aa0e4…a7edda958d4136
1 in β†’ 1 out8.2600 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.

8.038 Γ— 10⁹⁢(97-digit number)
80381906333137347066…97965202288867612160
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
8.038 Γ— 10⁹⁢(97-digit number)
80381906333137347066…97965202288867612159
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
8.038 Γ— 10⁹⁢(97-digit number)
80381906333137347066…97965202288867612161
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
1.607 Γ— 10⁹⁷(98-digit number)
16076381266627469413…95930404577735224319
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.607 Γ— 10⁹⁷(98-digit number)
16076381266627469413…95930404577735224321
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
3.215 Γ— 10⁹⁷(98-digit number)
32152762533254938826…91860809155470448639
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.215 Γ— 10⁹⁷(98-digit number)
32152762533254938826…91860809155470448641
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
6.430 Γ— 10⁹⁷(98-digit number)
64305525066509877653…83721618310940897279
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.430 Γ— 10⁹⁷(98-digit number)
64305525066509877653…83721618310940897281
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
1.286 Γ— 10⁹⁸(99-digit number)
12861105013301975530…67443236621881794559
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.286 Γ— 10⁹⁸(99-digit number)
12861105013301975530…67443236621881794561
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
2.572 Γ— 10⁹⁸(99-digit number)
25722210026603951061…34886473243763589119
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 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
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 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 3372456

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 e9238d9e0c61ddf23ea7b57732a0f23c75a1f10df9834c8cf9b6c3c3038043c2

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 #3,372,456 on Chainz β†—
Circulating Supply:57,937,647 XPMΒ·at block #6,836,670 Β· updates every 60s
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