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Home/Chain Registry/Block #3,088,808

Block #3,088,808

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 3/11/2019, 8:41:28 PM Β· Difficulty 11.0400 Β· 3,749,684 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
668d2b1d7725cf784645a4441ed3f56b9c54d974da94011328b656d2ee141cbf
View on Chainz β†—

Difficulty

11.039951

Transactions

1

Size

200 B

Version

2

Bits

0b0a3a3d

Nonce

2,123,993,377

Timestamp

3/11/2019, 8:41:28 PM

Confirmations

3,749,684

Merkle Root

319c010f520f0912616a989b073cfb185cb15c6ef843ca5ba6aa2bd1cc4bde11
Transactions (1)
Coinbase319c010f520f09…aa2bd1cc4bde11
1 in β†’ 1 out8.1900 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.

5.917 Γ— 10⁹⁴(95-digit number)
59173899275806419547…08010239307526057840
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
5.917 Γ— 10⁹⁴(95-digit number)
59173899275806419547…08010239307526057839
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.917 Γ— 10⁹⁴(95-digit number)
59173899275806419547…08010239307526057841
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
1.183 Γ— 10⁹⁡(96-digit number)
11834779855161283909…16020478615052115679
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.183 Γ— 10⁹⁡(96-digit number)
11834779855161283909…16020478615052115681
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
2.366 Γ— 10⁹⁡(96-digit number)
23669559710322567818…32040957230104231359
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.366 Γ— 10⁹⁡(96-digit number)
23669559710322567818…32040957230104231361
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
4.733 Γ— 10⁹⁡(96-digit number)
47339119420645135637…64081914460208462719
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.733 Γ— 10⁹⁡(96-digit number)
47339119420645135637…64081914460208462721
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
9.467 Γ— 10⁹⁡(96-digit number)
94678238841290271275…28163828920416925439
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
9.467 Γ— 10⁹⁡(96-digit number)
94678238841290271275…28163828920416925441
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
1.893 Γ— 10⁹⁢(97-digit number)
18935647768258054255…56327657840833850879
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 3088808

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 668d2b1d7725cf784645a4441ed3f56b9c54d974da94011328b656d2ee141cbf

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 #3,088,808 on Chainz β†—
Circulating Supply:57,952,208 XPMΒ·at block #6,838,491 Β· updates every 60s
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