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Home/Chain Registry/Block #2,114,369

Block #2,114,369

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 5/13/2017, 2:35:29 PM Β· Difficulty 10.9001 Β· 4,731,281 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
5a01587711afa91e4c389c04300aea536b9cfb806f206396c18b86e2c31aefef
View on Chainz β†—

Difficulty

10.900116

Transactions

2

Size

424 B

Version

2

Bits

0ae66dfc

Nonce

836,693,740

Timestamp

5/13/2017, 2:35:29 PM

Confirmations

4,731,281

Merkle Root

3a4e25214495811297844a86c44f3ac96c7c18702326492d82b293ad7bf5feb6
Transactions (2)
Coinbasec7949015d45a3e…67cb5ec0339074
1 in β†’ 1 out8.4100 XPM109 B
AZuYqo8F…b62JZfmY
aa770fd6d25a3a…8f80f9388205a0
1 in β†’ 2 out13208.4876 XPM226 B
AGWtLmiJ…BTtxbR5aAVgEanen…B9SFoAnx
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.

3.173 Γ— 10⁹³(94-digit number)
31736154168771569793…50076559803224367780
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
3.173 Γ— 10⁹³(94-digit number)
31736154168771569793…50076559803224367779
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.173 Γ— 10⁹³(94-digit number)
31736154168771569793…50076559803224367781
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
6.347 Γ— 10⁹³(94-digit number)
63472308337543139586…00153119606448735559
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.347 Γ— 10⁹³(94-digit number)
63472308337543139586…00153119606448735561
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
1.269 Γ— 10⁹⁴(95-digit number)
12694461667508627917…00306239212897471119
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.269 Γ— 10⁹⁴(95-digit number)
12694461667508627917…00306239212897471121
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
2.538 Γ— 10⁹⁴(95-digit number)
25388923335017255834…00612478425794942239
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.538 Γ— 10⁹⁴(95-digit number)
25388923335017255834…00612478425794942241
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
5.077 Γ— 10⁹⁴(95-digit number)
50777846670034511669…01224956851589884479
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.077 Γ— 10⁹⁴(95-digit number)
50777846670034511669…01224956851589884481
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 2114369

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 5a01587711afa91e4c389c04300aea536b9cfb806f206396c18b86e2c31aefef

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 #2,114,369 on Chainz β†—
Circulating Supply:58,009,649 XPMΒ·at block #6,845,649 Β· updates every 60s
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