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Block #356,889

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 1/13/2014, 1:11:40 AM Β· Difficulty 10.3829 Β· 6,443,320 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
e578d5097807c09bf4cffebb52a69a0626d822436a3d44195ce7e081f085b79b
View on Chainz β†—

Height

#356,889

Difficulty

10.382855

Transactions

1

Size

206 B

Version

2

Bits

0a6202c9

Nonce

486,542,903

Timestamp

1/13/2014, 1:11:40 AM

Confirmations

6,443,320

Merkle Root

7f386da868bf5185caad8f8083e0235826d97a82891277e44b6456a97648d26f
Transactions (1)
Coinbase7f386da868bf51…6456a97648d26f
1 in β†’ 1 out9.2600 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.

3.084 Γ— 10⁹⁡(96-digit number)
30845298800455120666…35277845728398782920
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
3.084 Γ— 10⁹⁡(96-digit number)
30845298800455120666…35277845728398782919
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.084 Γ— 10⁹⁡(96-digit number)
30845298800455120666…35277845728398782921
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
6.169 Γ— 10⁹⁡(96-digit number)
61690597600910241333…70555691456797565839
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.169 Γ— 10⁹⁡(96-digit number)
61690597600910241333…70555691456797565841
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
1.233 Γ— 10⁹⁢(97-digit number)
12338119520182048266…41111382913595131679
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.233 Γ— 10⁹⁢(97-digit number)
12338119520182048266…41111382913595131681
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
2.467 Γ— 10⁹⁢(97-digit number)
24676239040364096533…82222765827190263359
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.467 Γ— 10⁹⁢(97-digit number)
24676239040364096533…82222765827190263361
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
4.935 Γ— 10⁹⁢(97-digit number)
49352478080728193066…64445531654380526719
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.935 Γ— 10⁹⁢(97-digit number)
49352478080728193066…64445531654380526721
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 356889

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 e578d5097807c09bf4cffebb52a69a0626d822436a3d44195ce7e081f085b79b

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 #356,889 on Chainz β†—
Circulating Supply:57,645,741 XPMΒ·at block #6,800,208 Β· updates every 60s
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