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Block #169,528

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/18/2013, 2:14:53 AM Β· Difficulty 9.8674 Β· 6,676,122 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
b7e75202c1075667281f11a764e88f94d17a20dd18a650a2553608017afcac89
View on Chainz β†—

Height

#169,528

Difficulty

9.867446

Transactions

1

Size

198 B

Version

2

Bits

09de10f2

Nonce

331,664

Timestamp

9/18/2013, 2:14:53 AM

Confirmations

6,676,122

Merkle Root

2ad81a254c312cd57a343963c325ecdb20feceb9f4bb61cdb68192dc5c1b34ef
Transactions (1)
Coinbase2ad81a254c312c…8192dc5c1b34ef
1 in β†’ 1 out10.2600 XPM109 B
AdeGZSvc…o7B1Z3x3
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.

1.813 Γ— 10⁹³(94-digit number)
18132322746639370285…63579996007226248570
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
1.813 Γ— 10⁹³(94-digit number)
18132322746639370285…63579996007226248569
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.813 Γ— 10⁹³(94-digit number)
18132322746639370285…63579996007226248571
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
3.626 Γ— 10⁹³(94-digit number)
36264645493278740570…27159992014452497139
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.626 Γ— 10⁹³(94-digit number)
36264645493278740570…27159992014452497141
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
7.252 Γ— 10⁹³(94-digit number)
72529290986557481141…54319984028904994279
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
7.252 Γ— 10⁹³(94-digit number)
72529290986557481141…54319984028904994281
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
1.450 Γ— 10⁹⁴(95-digit number)
14505858197311496228…08639968057809988559
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.450 Γ— 10⁹⁴(95-digit number)
14505858197311496228…08639968057809988561
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
2.901 Γ— 10⁹⁴(95-digit number)
29011716394622992456…17279936115619977119
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 169528

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 b7e75202c1075667281f11a764e88f94d17a20dd18a650a2553608017afcac89

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 #169,528 on Chainz β†—
Circulating Supply:58,009,649 XPMΒ·at block #6,845,649 Β· updates every 60s
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