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Block #161,353

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/12/2013, 2:58:54 PM Β· Difficulty 9.8590 Β· 6,633,690 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
f5a29b3552273eecdad4cde562d490a1f27b9e957532e21c9ad21d47d54a6b2a
View on Chainz β†—

Height

#161,353

Difficulty

9.858962

Transactions

1

Size

197 B

Version

2

Bits

09dbe4f3

Nonce

44,189

Timestamp

9/12/2013, 2:58:54 PM

Confirmations

6,633,690

Merkle Root

2209e9623edd29c19907e8e740ba552d025b9f2eef7dca9207b95b68e4af855d
Transactions (1)
Coinbase2209e9623edd29…b95b68e4af855d
1 in β†’ 1 out10.2700 XPM109 B
AYbMkPmQ…MrnhaWgt
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.

4.503 Γ— 10⁹⁰(91-digit number)
45039650781975727187…15380749485488039520
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
4.503 Γ— 10⁹⁰(91-digit number)
45039650781975727187…15380749485488039519
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.503 Γ— 10⁹⁰(91-digit number)
45039650781975727187…15380749485488039521
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
9.007 Γ— 10⁹⁰(91-digit number)
90079301563951454375…30761498970976079039
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
9.007 Γ— 10⁹⁰(91-digit number)
90079301563951454375…30761498970976079041
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
1.801 Γ— 10⁹¹(92-digit number)
18015860312790290875…61522997941952158079
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.801 Γ— 10⁹¹(92-digit number)
18015860312790290875…61522997941952158081
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
3.603 Γ— 10⁹¹(92-digit number)
36031720625580581750…23045995883904316159
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.603 Γ— 10⁹¹(92-digit number)
36031720625580581750…23045995883904316161
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
7.206 Γ— 10⁹¹(92-digit number)
72063441251161163500…46091991767808632319
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 161353

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 f5a29b3552273eecdad4cde562d490a1f27b9e957532e21c9ad21d47d54a6b2a

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 #161,353 on Chainz β†—
Circulating Supply:57,604,383 XPMΒ·at block #6,795,042 Β· updates every 60s
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