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Home/Chain Registry/Block #3,226,027

Block #3,226,027

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 6/15/2019, 7:18:51 AM Β· Difficulty 11.0050 Β· 3,617,431 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
b2d31e9d48bb97857ea809267f065010fb3022c628079f7e27e85c766b799adb
View on Chainz β†—

Difficulty

11.005041

Transactions

1

Size

202 B

Version

2

Bits

0b014a65

Nonce

1,245,687,647

Timestamp

6/15/2019, 7:18:51 AM

Confirmations

3,617,431

Merkle Root

11dd77ec78821dcbacdd0f74ca3e60366bab8565c9583d6c2a16de8fb18e63a4
Transactions (1)
Coinbase11dd77ec78821d…16de8fb18e63a4
1 in β†’ 1 out8.2400 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.

2.124 Γ— 10⁹⁸(99-digit number)
21246806280326453609…35521918788868505600
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
2.124 Γ— 10⁹⁸(99-digit number)
21246806280326453609…35521918788868505599
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.124 Γ— 10⁹⁸(99-digit number)
21246806280326453609…35521918788868505601
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
4.249 Γ— 10⁹⁸(99-digit number)
42493612560652907218…71043837577737011199
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.249 Γ— 10⁹⁸(99-digit number)
42493612560652907218…71043837577737011201
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
8.498 Γ— 10⁹⁸(99-digit number)
84987225121305814436…42087675155474022399
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
8.498 Γ— 10⁹⁸(99-digit number)
84987225121305814436…42087675155474022401
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
1.699 Γ— 10⁹⁹(100-digit number)
16997445024261162887…84175350310948044799
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.699 Γ— 10⁹⁹(100-digit number)
16997445024261162887…84175350310948044801
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
3.399 Γ— 10⁹⁹(100-digit number)
33994890048522325774…68350700621896089599
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.399 Γ— 10⁹⁹(100-digit number)
33994890048522325774…68350700621896089601
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
6.798 Γ— 10⁹⁹(100-digit number)
67989780097044651548…36701401243792179199
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 3226027

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 b2d31e9d48bb97857ea809267f065010fb3022c628079f7e27e85c766b799adb

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 #3,226,027 on Chainz β†—
Circulating Supply:57,992,032 XPMΒ·at block #6,843,457 Β· updates every 60s
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