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Home/Chain Registry/Block #2,067,834

Block #2,067,834

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 4/12/2017, 1:05:31 PM Β· Difficulty 10.8555 Β· 4,759,027 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
6374df532f3230cb278352a47a17bf95e5056892a334283ebd454ecbe2b38ff0
View on Chainz β†—

Difficulty

10.855478

Transactions

1

Size

201 B

Version

2

Bits

0adb009e

Nonce

1,491,395,104

Timestamp

4/12/2017, 1:05:31 PM

Confirmations

4,759,027

Merkle Root

0c8a1d87bf8f616a92590239fa424ee9faf81daa7557af4cbe204b594861153f
Transactions (1)
Coinbase0c8a1d87bf8f61…204b594861153f
1 in β†’ 1 out8.4700 XPM110 B
AUVYkm3x…1gezLTKq
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.

4.338 Γ— 10⁹⁷(98-digit number)
43383527728875840847…29705799660585041920
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
4.338 Γ— 10⁹⁷(98-digit number)
43383527728875840847…29705799660585041919
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.338 Γ— 10⁹⁷(98-digit number)
43383527728875840847…29705799660585041921
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
8.676 Γ— 10⁹⁷(98-digit number)
86767055457751681694…59411599321170083839
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
8.676 Γ— 10⁹⁷(98-digit number)
86767055457751681694…59411599321170083841
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
1.735 Γ— 10⁹⁸(99-digit number)
17353411091550336338…18823198642340167679
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.735 Γ— 10⁹⁸(99-digit number)
17353411091550336338…18823198642340167681
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
3.470 Γ— 10⁹⁸(99-digit number)
34706822183100672677…37646397284680335359
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.470 Γ— 10⁹⁸(99-digit number)
34706822183100672677…37646397284680335361
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
6.941 Γ— 10⁹⁸(99-digit number)
69413644366201345355…75292794569360670719
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
6.941 Γ— 10⁹⁸(99-digit number)
69413644366201345355…75292794569360670721
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 2067834

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 6374df532f3230cb278352a47a17bf95e5056892a334283ebd454ecbe2b38ff0

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 #2,067,834 on Chainz β†—
Circulating Supply:57,859,057 XPMΒ·at block #6,826,860 Β· updates every 60s
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