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Home/Chain Registry/Block #2,826,940

Block #2,826,940

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 9/6/2018, 7:18:57 AM Β· Difficulty 11.7100 Β· 4,009,787 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
dc2d5706b03531ca566689497c11bf818cd37f785f31e1fe06e90d14858b9d50
View on Chainz β†—

Difficulty

11.710043

Transactions

1

Size

201 B

Version

2

Bits

0bb5c569

Nonce

876,712,216

Timestamp

9/6/2018, 7:18:57 AM

Confirmations

4,009,787

Merkle Root

bb0fa38e4c605bcb3ded20e1c92d5d0283f3fad36b88050409ba2e053fd0fa97
Transactions (1)
Coinbasebb0fa38e4c605b…ba2e053fd0fa97
1 in β†’ 1 out7.2800 XPM110 B
AVaAFaMt…Gnkr6oMQ
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.

3.776 Γ— 10⁹⁷(98-digit number)
37763737737268384546…02325351514832240640
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
3.776 Γ— 10⁹⁷(98-digit number)
37763737737268384546…02325351514832240639
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.776 Γ— 10⁹⁷(98-digit number)
37763737737268384546…02325351514832240641
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
7.552 Γ— 10⁹⁷(98-digit number)
75527475474536769093…04650703029664481279
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
7.552 Γ— 10⁹⁷(98-digit number)
75527475474536769093…04650703029664481281
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
1.510 Γ— 10⁹⁸(99-digit number)
15105495094907353818…09301406059328962559
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.510 Γ— 10⁹⁸(99-digit number)
15105495094907353818…09301406059328962561
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
3.021 Γ— 10⁹⁸(99-digit number)
30210990189814707637…18602812118657925119
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.021 Γ— 10⁹⁸(99-digit number)
30210990189814707637…18602812118657925121
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
6.042 Γ— 10⁹⁸(99-digit number)
60421980379629415274…37205624237315850239
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
6.042 Γ— 10⁹⁸(99-digit number)
60421980379629415274…37205624237315850241
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
1.208 Γ— 10⁹⁹(100-digit number)
12084396075925883054…74411248474631700479
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 2826940

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 dc2d5706b03531ca566689497c11bf818cd37f785f31e1fe06e90d14858b9d50

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 #2,826,940 on Chainz β†—
Circulating Supply:57,938,097 XPMΒ·at block #6,836,726 Β· updates every 60s
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