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Block #394,813

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 2/8/2014, 5:51:01 AM Β· Difficulty 10.4194 Β· 6,400,792 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
38d27399a090ef50194966da44224f253c718be31a9a0e7c2fe04bd78d8a3bd7
View on Chainz β†—

Height

#394,813

Difficulty

10.419432

Transactions

1

Size

201 B

Version

2

Bits

0a6b5fe4

Nonce

114,228

Timestamp

2/8/2014, 5:51:01 AM

Confirmations

6,400,792

Merkle Root

623e2d0a466198158ce7e1636cb0f1efbc29afce148a82a2b2cccc1d3a7c4e1e
Transactions (1)
Coinbase623e2d0a466198…cccc1d3a7c4e1e
1 in β†’ 1 out9.2000 XPM110 B
AeKNrjNj…1NEq95Ta
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.

1.487 Γ— 10⁹⁷(98-digit number)
14870218585430156573…52170781893308928000
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
1.487 Γ— 10⁹⁷(98-digit number)
14870218585430156573…52170781893308927999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.487 Γ— 10⁹⁷(98-digit number)
14870218585430156573…52170781893308928001
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
2.974 Γ— 10⁹⁷(98-digit number)
29740437170860313146…04341563786617855999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.974 Γ— 10⁹⁷(98-digit number)
29740437170860313146…04341563786617856001
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
5.948 Γ— 10⁹⁷(98-digit number)
59480874341720626293…08683127573235711999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.948 Γ— 10⁹⁷(98-digit number)
59480874341720626293…08683127573235712001
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
1.189 Γ— 10⁹⁸(99-digit number)
11896174868344125258…17366255146471423999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.189 Γ— 10⁹⁸(99-digit number)
11896174868344125258…17366255146471424001
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
2.379 Γ— 10⁹⁸(99-digit number)
23792349736688250517…34732510292942847999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.379 Γ— 10⁹⁸(99-digit number)
23792349736688250517…34732510292942848001
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 394813

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 38d27399a090ef50194966da44224f253c718be31a9a0e7c2fe04bd78d8a3bd7

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 #394,813 on Chainz β†—
Circulating Supply:57,608,904 XPMΒ·at block #6,795,604 Β· updates every 60s
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