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Block #175,240

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/22/2013, 4:02:32 AM Β· Difficulty 9.8637 Β· 6,651,712 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
c04e9a674809ad40b1e0eb24e424eff9c5303343ed1b3d3efb1d74b1dabfd395
View on Chainz β†—

Height

#175,240

Difficulty

9.863713

Transactions

1

Size

200 B

Version

2

Bits

09dd1c4e

Nonce

214,572

Timestamp

9/22/2013, 4:02:32 AM

Confirmations

6,651,712

Merkle Root

f6cf18ad2f68e9f0c82649132c1f377c8d3ee7c5f35671090b6cf8cb1002322d
Transactions (1)
Coinbasef6cf18ad2f68e9…6cf8cb1002322d
1 in β†’ 1 out10.2600 XPM110 B
AN4MMKBX…naqNeHQo
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.

5.924 Γ— 10⁹⁴(95-digit number)
59245886322141469560…87482309762653122240
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
5.924 Γ— 10⁹⁴(95-digit number)
59245886322141469560…87482309762653122239
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.924 Γ— 10⁹⁴(95-digit number)
59245886322141469560…87482309762653122241
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
1.184 Γ— 10⁹⁡(96-digit number)
11849177264428293912…74964619525306244479
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.184 Γ— 10⁹⁡(96-digit number)
11849177264428293912…74964619525306244481
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
2.369 Γ— 10⁹⁡(96-digit number)
23698354528856587824…49929239050612488959
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.369 Γ— 10⁹⁡(96-digit number)
23698354528856587824…49929239050612488961
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
4.739 Γ— 10⁹⁡(96-digit number)
47396709057713175648…99858478101224977919
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.739 Γ— 10⁹⁡(96-digit number)
47396709057713175648…99858478101224977921
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
9.479 Γ— 10⁹⁡(96-digit number)
94793418115426351297…99716956202449955839
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 175240

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 c04e9a674809ad40b1e0eb24e424eff9c5303343ed1b3d3efb1d74b1dabfd395

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 #175,240 on Chainz β†—
Circulating Supply:57,859,792 XPMΒ·at block #6,826,951 Β· updates every 60s
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