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Home/Chain Registry/Block #1,113,481

Block #1,113,481

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 6/17/2015, 4:43:57 PM Β· Difficulty 10.9052 Β· 5,725,948 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
d3e2515e0bba2ddf9eef9f8e89dfc33b76772b27e8bd24b676e5f940b5c5ca6e
View on Chainz β†—

Difficulty

10.905240

Transactions

1

Size

201 B

Version

2

Bits

0ae7bdd7

Nonce

1,066,623,853

Timestamp

6/17/2015, 4:43:57 PM

Confirmations

5,725,948

Merkle Root

8495cf7a273aca0323f93709c3ab5b725741b8a0fd3879ffe7fc4f8f7f8d882b
Transactions (1)
Coinbase8495cf7a273aca…fc4f8f7f8d882b
1 in β†’ 1 out8.4000 XPM110 B
AUULQ3ce…Z9BBVStm
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.

4.347 Γ— 10⁹⁷(98-digit number)
43470021489121942775…13683723739717959680
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
4.347 Γ— 10⁹⁷(98-digit number)
43470021489121942775…13683723739717959679
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.347 Γ— 10⁹⁷(98-digit number)
43470021489121942775…13683723739717959681
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
8.694 Γ— 10⁹⁷(98-digit number)
86940042978243885551…27367447479435919359
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
8.694 Γ— 10⁹⁷(98-digit number)
86940042978243885551…27367447479435919361
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
1.738 Γ— 10⁹⁸(99-digit number)
17388008595648777110…54734894958871838719
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.738 Γ— 10⁹⁸(99-digit number)
17388008595648777110…54734894958871838721
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
3.477 Γ— 10⁹⁸(99-digit number)
34776017191297554220…09469789917743677439
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.477 Γ— 10⁹⁸(99-digit number)
34776017191297554220…09469789917743677441
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
6.955 Γ— 10⁹⁸(99-digit number)
69552034382595108440…18939579835487354879
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
6.955 Γ— 10⁹⁸(99-digit number)
69552034382595108440…18939579835487354881
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 1113481

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 d3e2515e0bba2ddf9eef9f8e89dfc33b76772b27e8bd24b676e5f940b5c5ca6e

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 #1,113,481 on Chainz β†—
Circulating Supply:57,959,720 XPMΒ·at block #6,839,428 Β· updates every 60s
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