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Block #381,596

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 1/30/2014, 3:15:39 AM Β· Difficulty 10.4026 Β· 6,416,587 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
6566d62def12642497e0ab5164df1b03f38d12d2058ecf139439fe182e36217b
View on Chainz β†—

Height

#381,596

Difficulty

10.402650

Transactions

1

Size

207 B

Version

2

Bits

0a67140d

Nonce

438,310

Timestamp

1/30/2014, 3:15:39 AM

Confirmations

6,416,587

Merkle Root

36e393eb8a4add4d1fabb18fa6c930caf495d1a95ffbac5b7e4e8b0d610989d0
Transactions (1)
Coinbase36e393eb8a4add…4e8b0d610989d0
1 in β†’ 1 out9.2300 XPM116 B
AbwWkWZt…kawDhufa
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.

1.542 Γ— 10⁹⁸(99-digit number)
15426022899387825294…32100174213921896920
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
1.542 Γ— 10⁹⁸(99-digit number)
15426022899387825294…32100174213921896919
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.542 Γ— 10⁹⁸(99-digit number)
15426022899387825294…32100174213921896921
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
3.085 Γ— 10⁹⁸(99-digit number)
30852045798775650589…64200348427843793839
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.085 Γ— 10⁹⁸(99-digit number)
30852045798775650589…64200348427843793841
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
6.170 Γ— 10⁹⁸(99-digit number)
61704091597551301178…28400696855687587679
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.170 Γ— 10⁹⁸(99-digit number)
61704091597551301178…28400696855687587681
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
1.234 Γ— 10⁹⁹(100-digit number)
12340818319510260235…56801393711375175359
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.234 Γ— 10⁹⁹(100-digit number)
12340818319510260235…56801393711375175361
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
2.468 Γ— 10⁹⁹(100-digit number)
24681636639020520471…13602787422750350719
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.468 Γ— 10⁹⁹(100-digit number)
24681636639020520471…13602787422750350721
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 381596

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 6566d62def12642497e0ab5164df1b03f38d12d2058ecf139439fe182e36217b

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 #381,596 on Chainz β†—
Circulating Supply:57,629,467 XPMΒ·at block #6,798,182 Β· updates every 60s
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