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Block #351,494

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 1/9/2014, 5:59:42 PM Β· Difficulty 10.2958 Β· 6,462,592 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
aa10f562dbc7801c0d38db77d2db41511be2ed39b35f3df698c2f99df8cac51e
View on Chainz β†—

Height

#351,494

Difficulty

10.295803

Transactions

1

Size

206 B

Version

2

Bits

0a4bb9bc

Nonce

16,781,858

Timestamp

1/9/2014, 5:59:42 PM

Confirmations

6,462,592

Merkle Root

e50016f23614daa38b656453b139b49faf8f5f42c364bcd1b6f258affa940843
Transactions (1)
Coinbasee50016f23614da…f258affa940843
1 in β†’ 1 out9.4200 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.

5.424 Γ— 10⁹⁡(96-digit number)
54240633900937286068…83318656412480982080
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
5.424 Γ— 10⁹⁡(96-digit number)
54240633900937286068…83318656412480982079
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.424 Γ— 10⁹⁡(96-digit number)
54240633900937286068…83318656412480982081
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
1.084 Γ— 10⁹⁢(97-digit number)
10848126780187457213…66637312824961964159
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.084 Γ— 10⁹⁢(97-digit number)
10848126780187457213…66637312824961964161
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
2.169 Γ— 10⁹⁢(97-digit number)
21696253560374914427…33274625649923928319
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.169 Γ— 10⁹⁢(97-digit number)
21696253560374914427…33274625649923928321
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
4.339 Γ— 10⁹⁢(97-digit number)
43392507120749828854…66549251299847856639
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.339 Γ— 10⁹⁢(97-digit number)
43392507120749828854…66549251299847856641
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
8.678 Γ— 10⁹⁢(97-digit number)
86785014241499657709…33098502599695713279
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
8.678 Γ— 10⁹⁢(97-digit number)
86785014241499657709…33098502599695713281
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 351494

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 aa10f562dbc7801c0d38db77d2db41511be2ed39b35f3df698c2f99df8cac51e

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 #351,494 on Chainz β†—
Circulating Supply:57,756,769 XPMΒ·at block #6,814,085 Β· updates every 60s
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