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Block #163,964

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/14/2013, 8:48:34 AM Β· Difficulty 9.8619 Β· 6,660,830 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
dd8319f337b31e8a3fcfd69aca87c5180f92f1af8dcf383b3240019e91ca1609
View on Chainz β†—

Height

#163,964

Difficulty

9.861892

Transactions

1

Size

198 B

Version

2

Bits

09dca4f5

Nonce

320,565

Timestamp

9/14/2013, 8:48:34 AM

Confirmations

6,660,830

Merkle Root

ee539a64abe5f69f534f4ec4b9820e32d5032d48b7fee92b5d35fe7f6cc01e76
Transactions (1)
Coinbaseee539a64abe5f6…35fe7f6cc01e76
1 in β†’ 1 out10.2700 XPM109 B
ATfkLTJT…R6ZBdUL9
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.

7.544 Γ— 10⁹²(93-digit number)
75441993410836525644…96379896695159068600
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
7.544 Γ— 10⁹²(93-digit number)
75441993410836525644…96379896695159068599
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
7.544 Γ— 10⁹²(93-digit number)
75441993410836525644…96379896695159068601
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
1.508 Γ— 10⁹³(94-digit number)
15088398682167305128…92759793390318137199
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.508 Γ— 10⁹³(94-digit number)
15088398682167305128…92759793390318137201
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
3.017 Γ— 10⁹³(94-digit number)
30176797364334610257…85519586780636274399
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.017 Γ— 10⁹³(94-digit number)
30176797364334610257…85519586780636274401
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
6.035 Γ— 10⁹³(94-digit number)
60353594728669220515…71039173561272548799
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.035 Γ— 10⁹³(94-digit number)
60353594728669220515…71039173561272548801
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
1.207 Γ— 10⁹⁴(95-digit number)
12070718945733844103…42078347122545097599
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 163964

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 dd8319f337b31e8a3fcfd69aca87c5180f92f1af8dcf383b3240019e91ca1609

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 #163,964 on Chainz β†—
Circulating Supply:57,842,427 XPMΒ·at block #6,824,793 Β· updates every 60s
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