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Home/Chain Registry/Block #3,244,037

Block #3,244,037

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 6/28/2019, 2:15:25 AM Β· Difficulty 11.0061 Β· 3,598,863 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
1b536d55761df54237c9615014343f1e31f4e4d089c0fd0e9a438364999ea3cf
View on Chainz β†—

Difficulty

11.006070

Transactions

1

Size

200 B

Version

2

Bits

0b018dcc

Nonce

1,526,415,245

Timestamp

6/28/2019, 2:15:25 AM

Confirmations

3,598,863

Merkle Root

83ca5d8fa389c87b616ca15c98f9005c022f5b0c47fd5996df25bc283381731c
Transactions (1)
Coinbase83ca5d8fa389c8…25bc283381731c
1 in β†’ 1 out8.2400 XPM110 B
ARbm48qR…9xQc8DBX
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.

4.933 Γ— 10⁹³(94-digit number)
49331567981681672446…51241370170726413440
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
4.933 Γ— 10⁹³(94-digit number)
49331567981681672446…51241370170726413439
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.933 Γ— 10⁹³(94-digit number)
49331567981681672446…51241370170726413441
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
9.866 Γ— 10⁹³(94-digit number)
98663135963363344892…02482740341452826879
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
9.866 Γ— 10⁹³(94-digit number)
98663135963363344892…02482740341452826881
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
1.973 Γ— 10⁹⁴(95-digit number)
19732627192672668978…04965480682905653759
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.973 Γ— 10⁹⁴(95-digit number)
19732627192672668978…04965480682905653761
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
3.946 Γ— 10⁹⁴(95-digit number)
39465254385345337957…09930961365811307519
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.946 Γ— 10⁹⁴(95-digit number)
39465254385345337957…09930961365811307521
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
7.893 Γ— 10⁹⁴(95-digit number)
78930508770690675914…19861922731622615039
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
7.893 Γ— 10⁹⁴(95-digit number)
78930508770690675914…19861922731622615041
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
1.578 Γ— 10⁹⁡(96-digit number)
15786101754138135182…39723845463245230079
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 3244037

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 1b536d55761df54237c9615014343f1e31f4e4d089c0fd0e9a438364999ea3cf

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 #3,244,037 on Chainz β†—
Circulating Supply:57,987,548 XPMΒ·at block #6,842,899 Β· updates every 60s
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