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Block #168,065

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/17/2013, 1:16:14 AM Β· Difficulty 9.8684 Β· 6,657,981 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
9a213bf161ffcb40bd4865b98c8bf3cea1100f686876ae5d0adff3cc9de122eb
View on Chainz β†—

Height

#168,065

Difficulty

9.868361

Transactions

2

Size

424 B

Version

2

Bits

09de4ce5

Nonce

172,301

Timestamp

9/17/2013, 1:16:14 AM

Confirmations

6,657,981

Merkle Root

c680ef9307f5bf91f10dab8857a8dc612d46e6e9146d02bbe71163290d2ad325
Transactions (2)
Coinbased3accc746daec0…75952feb89aa4f
1 in β†’ 1 out10.2600 XPM109 B
AG9ocqwr…2MwsAk9z
48b906c1ffd91f…e083b737d1c1be
1 in β†’ 2 out5.6249 XPM226 B
Abp8DVB6…U9coefrmAH7diWGo…V2EhB1BM
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.

8.731 Γ— 10⁹²(93-digit number)
87311078454530994126…71229549057900795200
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
8.731 Γ— 10⁹²(93-digit number)
87311078454530994126…71229549057900795199
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
8.731 Γ— 10⁹²(93-digit number)
87311078454530994126…71229549057900795201
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
1.746 Γ— 10⁹³(94-digit number)
17462215690906198825…42459098115801590399
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.746 Γ— 10⁹³(94-digit number)
17462215690906198825…42459098115801590401
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
3.492 Γ— 10⁹³(94-digit number)
34924431381812397650…84918196231603180799
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.492 Γ— 10⁹³(94-digit number)
34924431381812397650…84918196231603180801
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
6.984 Γ— 10⁹³(94-digit number)
69848862763624795300…69836392463206361599
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.984 Γ— 10⁹³(94-digit number)
69848862763624795300…69836392463206361601
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
1.396 Γ— 10⁹⁴(95-digit number)
13969772552724959060…39672784926412723199
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9
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 168065

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 9a213bf161ffcb40bd4865b98c8bf3cea1100f686876ae5d0adff3cc9de122eb

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 #168,065 on Chainz β†—
Circulating Supply:57,852,494 XPMΒ·at block #6,826,045 Β· updates every 60s
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