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Home/Chain Registry/Block #2,150,166

Block #2,150,166

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 6/7/2017, 1:21:38 PM Β· Difficulty 10.8987 Β· 4,695,485 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
477156a77447422193d8dd448647555a2859e07996abe1f8373a8e2ae202359e
View on Chainz β†—

Difficulty

10.898686

Transactions

1

Size

201 B

Version

2

Bits

0ae61047

Nonce

1,481,209,975

Timestamp

6/7/2017, 1:21:38 PM

Confirmations

4,695,485

Merkle Root

2ec93b85a2a6836b3b2bc7825d22b812aef1df19ad6ef1c7e26f8fb10d412514
Transactions (1)
Coinbase2ec93b85a2a683…6f8fb10d412514
1 in β†’ 1 out8.4100 XPM109 B
AcJwzwei…12gy1BLa
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.

4.309 Γ— 10⁹⁸(99-digit number)
43092536848524342194…65004667999348326400
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
4.309 Γ— 10⁹⁸(99-digit number)
43092536848524342194…65004667999348326399
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.309 Γ— 10⁹⁸(99-digit number)
43092536848524342194…65004667999348326401
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
8.618 Γ— 10⁹⁸(99-digit number)
86185073697048684388…30009335998696652799
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
8.618 Γ— 10⁹⁸(99-digit number)
86185073697048684388…30009335998696652801
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
1.723 Γ— 10⁹⁹(100-digit number)
17237014739409736877…60018671997393305599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.723 Γ— 10⁹⁹(100-digit number)
17237014739409736877…60018671997393305601
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
3.447 Γ— 10⁹⁹(100-digit number)
34474029478819473755…20037343994786611199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.447 Γ— 10⁹⁹(100-digit number)
34474029478819473755…20037343994786611201
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
6.894 Γ— 10⁹⁹(100-digit number)
68948058957638947510…40074687989573222399
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
6.894 Γ— 10⁹⁹(100-digit number)
68948058957638947510…40074687989573222401
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
1.378 Γ— 10¹⁰⁰(101-digit number)
13789611791527789502…80149375979146444799
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 2150166

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 477156a77447422193d8dd448647555a2859e07996abe1f8373a8e2ae202359e

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 #2,150,166 on Chainz β†—
Circulating Supply:58,009,657 XPMΒ·at block #6,845,650 Β· updates every 60s
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