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Block #1,346,512

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 11/28/2015, 10:43:38 PM Β· Difficulty 10.8224 Β· 5,464,159 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
9b8febb244daa14ea2e1ced36ec84aa6bb502e0a1baed33daaee22fc656bd42e
View on Chainz β†—

Difficulty

10.822408

Transactions

1

Size

199 B

Version

2

Bits

0ad2894f

Nonce

560,470,320

Timestamp

11/28/2015, 10:43:38 PM

Confirmations

5,464,159

Merkle Root

b15f483028dd46cca22364cc5424817d311e4b9890604b30b05dfc91d36fc59c
Transactions (1)
Coinbaseb15f483028dd46…5dfc91d36fc59c
1 in β†’ 1 out8.5200 XPM109 B
AHDarhh7…6XEA1cRz
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.

5.244 Γ— 10⁹⁡(96-digit number)
52442181296253795827…14218166386700902880
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
5.244 Γ— 10⁹⁡(96-digit number)
52442181296253795827…14218166386700902879
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.244 Γ— 10⁹⁡(96-digit number)
52442181296253795827…14218166386700902881
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
1.048 Γ— 10⁹⁢(97-digit number)
10488436259250759165…28436332773401805759
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.048 Γ— 10⁹⁢(97-digit number)
10488436259250759165…28436332773401805761
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
2.097 Γ— 10⁹⁢(97-digit number)
20976872518501518331…56872665546803611519
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.097 Γ— 10⁹⁢(97-digit number)
20976872518501518331…56872665546803611521
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
4.195 Γ— 10⁹⁢(97-digit number)
41953745037003036662…13745331093607223039
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.195 Γ— 10⁹⁢(97-digit number)
41953745037003036662…13745331093607223041
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
8.390 Γ— 10⁹⁢(97-digit number)
83907490074006073324…27490662187214446079
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
8.390 Γ— 10⁹⁢(97-digit number)
83907490074006073324…27490662187214446081
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 1346512

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 9b8febb244daa14ea2e1ced36ec84aa6bb502e0a1baed33daaee22fc656bd42e

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 #1,346,512 on Chainz β†—
Circulating Supply:57,729,459 XPMΒ·at block #6,810,670 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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