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Block #350,407

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 1/9/2014, 12:47:40 AM Β· Difficulty 10.2878 Β· 6,450,467 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
1b2bd741d56d2bebf13f92725b3c245289b79c2dd8af6e700dc3ab08b142bffe
View on Chainz β†—

Height

#350,407

Difficulty

10.287820

Transactions

1

Size

201 B

Version

2

Bits

0a49ae99

Nonce

3,844

Timestamp

1/9/2014, 12:47:40 AM

Confirmations

6,450,467

Merkle Root

66415c5f7409e3e52665240a7a3df32a02a63d73b76a28607318d02573f737ce
Transactions (1)
Coinbase66415c5f7409e3…18d02573f737ce
1 in β†’ 1 out9.4300 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.

2.531 Γ— 10⁹⁢(97-digit number)
25313760886485029706…47628930415719347200
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
2.531 Γ— 10⁹⁢(97-digit number)
25313760886485029706…47628930415719347199
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.531 Γ— 10⁹⁢(97-digit number)
25313760886485029706…47628930415719347201
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
5.062 Γ— 10⁹⁢(97-digit number)
50627521772970059412…95257860831438694399
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.062 Γ— 10⁹⁢(97-digit number)
50627521772970059412…95257860831438694401
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
1.012 Γ— 10⁹⁷(98-digit number)
10125504354594011882…90515721662877388799
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.012 Γ— 10⁹⁷(98-digit number)
10125504354594011882…90515721662877388801
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
2.025 Γ— 10⁹⁷(98-digit number)
20251008709188023765…81031443325754777599
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.025 Γ— 10⁹⁷(98-digit number)
20251008709188023765…81031443325754777601
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
4.050 Γ— 10⁹⁷(98-digit number)
40502017418376047530…62062886651509555199
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.050 Γ— 10⁹⁷(98-digit number)
40502017418376047530…62062886651509555201
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 350407

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 1b2bd741d56d2bebf13f92725b3c245289b79c2dd8af6e700dc3ab08b142bffe

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 #350,407 on Chainz β†—
Circulating Supply:57,651,049 XPMΒ·at block #6,800,873 Β· updates every 60s
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