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Block #294,834

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 12/5/2013, 2:36:05 AM Β· Difficulty 9.9912 Β· 6,517,412 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
69d9cf98650b7935850d4feef8cc02b5e73f6c76fdc8454d9f7847cf119025a8
View on Chainz β†—

Height

#294,834

Difficulty

9.991164

Transactions

1

Size

199 B

Version

2

Bits

09fdbcee

Nonce

142,901

Timestamp

12/5/2013, 2:36:05 AM

Confirmations

6,517,412

Merkle Root

5b76c22705bddbc133f5e9111d4caccdb6973e9cd2e2709c7514ee1bec20ccea
Transactions (1)
Coinbase5b76c22705bddb…14ee1bec20ccea
1 in β†’ 1 out10.0000 XPM109 B
AWP61hEi…1dnDFsZW
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.

2.307 Γ— 10⁹⁡(96-digit number)
23070062671289266457…43842941408316315520
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
2.307 Γ— 10⁹⁡(96-digit number)
23070062671289266457…43842941408316315519
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.307 Γ— 10⁹⁡(96-digit number)
23070062671289266457…43842941408316315521
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
4.614 Γ— 10⁹⁡(96-digit number)
46140125342578532914…87685882816632631039
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.614 Γ— 10⁹⁡(96-digit number)
46140125342578532914…87685882816632631041
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
9.228 Γ— 10⁹⁡(96-digit number)
92280250685157065829…75371765633265262079
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
9.228 Γ— 10⁹⁡(96-digit number)
92280250685157065829…75371765633265262081
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
1.845 Γ— 10⁹⁢(97-digit number)
18456050137031413165…50743531266530524159
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.845 Γ— 10⁹⁢(97-digit number)
18456050137031413165…50743531266530524161
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
3.691 Γ— 10⁹⁢(97-digit number)
36912100274062826331…01487062533061048319
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.691 Γ— 10⁹⁢(97-digit number)
36912100274062826331…01487062533061048321
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 294834

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 69d9cf98650b7935850d4feef8cc02b5e73f6c76fdc8454d9f7847cf119025a8

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 #294,834 on Chainz β†—
Circulating Supply:57,741,987 XPMΒ·at block #6,812,245 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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