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Block #173,091

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/20/2013, 5:41:19 PM Β· Difficulty 9.8612 Β· 6,622,866 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
ac355d93767eaaa305ae92b4fec0bc552950bccd50577aab82f78941feedbcc2
View on Chainz β†—

Height

#173,091

Difficulty

9.861222

Transactions

1

Size

202 B

Version

2

Bits

09dc7904

Nonce

218,105,881

Timestamp

9/20/2013, 5:41:19 PM

Confirmations

6,622,866

Merkle Root

daabeee76429a70fb048639724837cacd1838e001814bf6e344d7b72cf70f727
Transactions (1)
Coinbasedaabeee76429a7…4d7b72cf70f727
1 in β†’ 1 out10.2700 XPM112 B
AcLBm5Z9…S683d7c3
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.

2.154 Γ— 10⁹⁴(95-digit number)
21545091030965608302…70474409256869390960
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
2.154 Γ— 10⁹⁴(95-digit number)
21545091030965608302…70474409256869390959
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.154 Γ— 10⁹⁴(95-digit number)
21545091030965608302…70474409256869390961
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
4.309 Γ— 10⁹⁴(95-digit number)
43090182061931216605…40948818513738781919
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.309 Γ— 10⁹⁴(95-digit number)
43090182061931216605…40948818513738781921
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
8.618 Γ— 10⁹⁴(95-digit number)
86180364123862433211…81897637027477563839
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
8.618 Γ— 10⁹⁴(95-digit number)
86180364123862433211…81897637027477563841
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
1.723 Γ— 10⁹⁡(96-digit number)
17236072824772486642…63795274054955127679
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.723 Γ— 10⁹⁡(96-digit number)
17236072824772486642…63795274054955127681
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
3.447 Γ— 10⁹⁡(96-digit number)
34472145649544973284…27590548109910255359
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 173091

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 ac355d93767eaaa305ae92b4fec0bc552950bccd50577aab82f78941feedbcc2

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 #173,091 on Chainz β†—
Circulating Supply:57,611,746 XPMΒ·at block #6,795,956 Β· updates every 60s
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