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Block #334,000

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 12/29/2013, 4:47:43 AM Β· Difficulty 10.1591 Β· 6,492,394 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
9d46d7a0fbe57ba9c16d88ab8d7d0d84683865cfe3dc5c64835583f13e6b5a27
View on Chainz β†—

Height

#334,000

Difficulty

10.159128

Transactions

1

Size

206 B

Version

2

Bits

0a28bca1

Nonce

24,578

Timestamp

12/29/2013, 4:47:43 AM

Confirmations

6,492,394

Merkle Root

43e3bdb33fe419f663094dcf0a5bcf7a8893abffc4380dbaf815f28ecf6e5014
Transactions (1)
Coinbase43e3bdb33fe419…15f28ecf6e5014
1 in β†’ 1 out9.6700 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.

1.156 Γ— 10⁹⁴(95-digit number)
11560761019853528456…80800351270502595200
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
1.156 Γ— 10⁹⁴(95-digit number)
11560761019853528456…80800351270502595199
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.156 Γ— 10⁹⁴(95-digit number)
11560761019853528456…80800351270502595201
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
2.312 Γ— 10⁹⁴(95-digit number)
23121522039707056912…61600702541005190399
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.312 Γ— 10⁹⁴(95-digit number)
23121522039707056912…61600702541005190401
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
4.624 Γ— 10⁹⁴(95-digit number)
46243044079414113824…23201405082010380799
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.624 Γ— 10⁹⁴(95-digit number)
46243044079414113824…23201405082010380801
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
9.248 Γ— 10⁹⁴(95-digit number)
92486088158828227649…46402810164020761599
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
9.248 Γ— 10⁹⁴(95-digit number)
92486088158828227649…46402810164020761601
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
1.849 Γ— 10⁹⁡(96-digit number)
18497217631765645529…92805620328041523199
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.849 Γ— 10⁹⁡(96-digit number)
18497217631765645529…92805620328041523201
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 334000

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 9d46d7a0fbe57ba9c16d88ab8d7d0d84683865cfe3dc5c64835583f13e6b5a27

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 #334,000 on Chainz β†—
Circulating Supply:57,855,291 XPMΒ·at block #6,826,393 Β· updates every 60s
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