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Block #176,757

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/23/2013, 4:22:20 AM Β· Difficulty 9.8653 Β· 6,648,697 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
20d47e080963e495e1a4622656a081d95e1fd06f5e98177d3f1221750ae92bae
View on Chainz β†—

Height

#176,757

Difficulty

9.865322

Transactions

2

Size

355 B

Version

2

Bits

09dd85b7

Nonce

35,411

Timestamp

9/23/2013, 4:22:20 AM

Confirmations

6,648,697

Merkle Root

41a0a43498614bb190025b61bbdfad8143add10cb6e1687554ddcf8156fdd839
Transactions (2)
Coinbaseca7493e2646744…6b65838b3fb154
1 in β†’ 1 out10.2700 XPM110 B
AW5HuGnN…DzGoJ8N8
a42312f2548d01…94d3bad7ceed80
1 in β†’ 1 out10.2800 XPM157 B
AYTevZvJ…n8JMVQpg
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.

4.641 Γ— 10⁸⁹(90-digit number)
46417510668832960062…70222232572135280640
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
4.641 Γ— 10⁸⁹(90-digit number)
46417510668832960062…70222232572135280639
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.641 Γ— 10⁸⁹(90-digit number)
46417510668832960062…70222232572135280641
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
9.283 Γ— 10⁸⁹(90-digit number)
92835021337665920125…40444465144270561279
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
9.283 Γ— 10⁸⁹(90-digit number)
92835021337665920125…40444465144270561281
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
1.856 Γ— 10⁹⁰(91-digit number)
18567004267533184025…80888930288541122559
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.856 Γ— 10⁹⁰(91-digit number)
18567004267533184025…80888930288541122561
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
3.713 Γ— 10⁹⁰(91-digit number)
37134008535066368050…61777860577082245119
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.713 Γ— 10⁹⁰(91-digit number)
37134008535066368050…61777860577082245121
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
7.426 Γ— 10⁹⁰(91-digit number)
74268017070132736100…23555721154164490239
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 176757

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 20d47e080963e495e1a4622656a081d95e1fd06f5e98177d3f1221750ae92bae

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 #176,757 on Chainz β†—
Circulating Supply:57,847,737 XPMΒ·at block #6,825,453 Β· updates every 60s
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