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Home/Chain Registry/Block #2,096,776

Block #2,096,776

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/2/2017, 5:52:51 AM Β· Difficulty 10.8719 Β· 4,748,414 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
0c756ea016b32346a79ae4b19b46b421c0e171cd55aede8cd7cf07ca20130064
View on Chainz β†—

Difficulty

10.871903

Transactions

2

Size

425 B

Version

2

Bits

0adf3501

Nonce

674,973,878

Timestamp

5/2/2017, 5:52:51 AM

Confirmations

4,748,414

Merkle Root

9220e6c50128ca70bf18975c075af9b7ecf80a43ca98313c369109b75583e31c
Transactions (2)
Coinbaseb7905af2864d78…212585a3df855a
1 in β†’ 1 out8.4600 XPM109 B
AYHSLhBW…CESV4opt
e45471f549fe30…0275b635c19580
1 in β†’ 2 out78098.2409 XPM226 B
ASKQZyaB…YB6o6NzTAV7wXFAb…BP2DYDKi
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.

9.291 Γ— 10⁹³(94-digit number)
92915611265743111892…78728546068215697440
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
9.291 Γ— 10⁹³(94-digit number)
92915611265743111892…78728546068215697439
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
9.291 Γ— 10⁹³(94-digit number)
92915611265743111892…78728546068215697441
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
1.858 Γ— 10⁹⁴(95-digit number)
18583122253148622378…57457092136431394879
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.858 Γ— 10⁹⁴(95-digit number)
18583122253148622378…57457092136431394881
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
3.716 Γ— 10⁹⁴(95-digit number)
37166244506297244757…14914184272862789759
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.716 Γ— 10⁹⁴(95-digit number)
37166244506297244757…14914184272862789761
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
7.433 Γ— 10⁹⁴(95-digit number)
74332489012594489514…29828368545725579519
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
7.433 Γ— 10⁹⁴(95-digit number)
74332489012594489514…29828368545725579521
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
1.486 Γ— 10⁹⁡(96-digit number)
14866497802518897902…59656737091451159039
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.486 Γ— 10⁹⁡(96-digit number)
14866497802518897902…59656737091451159041
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
2.973 Γ— 10⁹⁡(96-digit number)
29732995605037795805…19313474182902318079
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11
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 2096776

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 0c756ea016b32346a79ae4b19b46b421c0e171cd55aede8cd7cf07ca20130064

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 #2,096,776 on Chainz β†—
Circulating Supply:58,005,950 XPMΒ·at block #6,845,189 Β· updates every 60s
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