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Home/Chain Registry/Block #2,093,942

Block #2,093,942

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 4/30/2017, 7:07:45 AM Β· Difficulty 10.8711 Β· 4,750,486 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
45fb7523d333360a937b718fba9505cc6432015d65cb034bd77c6f3decc9f15a
View on Chainz β†—

Difficulty

10.871062

Transactions

1

Size

200 B

Version

2

Bits

0adefde4

Nonce

162,132,852

Timestamp

4/30/2017, 7:07:45 AM

Confirmations

4,750,486

Merkle Root

c21f181a7a3f93db696f202f06d62a74be1c8f1be58d8f0ab1ff5d59ccd4c7b6
Transactions (1)
Coinbasec21f181a7a3f93…ff5d59ccd4c7b6
1 in β†’ 1 out8.4500 XPM109 B
AVdn4RNi…b9FbcJMp
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.

1.062 Γ— 10⁹⁷(98-digit number)
10621472242165829434…11280802155545559040
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
1.062 Γ— 10⁹⁷(98-digit number)
10621472242165829434…11280802155545559039
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.062 Γ— 10⁹⁷(98-digit number)
10621472242165829434…11280802155545559041
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
2.124 Γ— 10⁹⁷(98-digit number)
21242944484331658868…22561604311091118079
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.124 Γ— 10⁹⁷(98-digit number)
21242944484331658868…22561604311091118081
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
4.248 Γ— 10⁹⁷(98-digit number)
42485888968663317737…45123208622182236159
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.248 Γ— 10⁹⁷(98-digit number)
42485888968663317737…45123208622182236161
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
8.497 Γ— 10⁹⁷(98-digit number)
84971777937326635475…90246417244364472319
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
8.497 Γ— 10⁹⁷(98-digit number)
84971777937326635475…90246417244364472321
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
1.699 Γ— 10⁹⁸(99-digit number)
16994355587465327095…80492834488728944639
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.699 Γ— 10⁹⁸(99-digit number)
16994355587465327095…80492834488728944641
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 2093942

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 45fb7523d333360a937b718fba9505cc6432015d65cb034bd77c6f3decc9f15a

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 #2,093,942 on Chainz β†—
Circulating Supply:57,999,821 XPMΒ·at block #6,844,427 Β· updates every 60s
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