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Block #172,759

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/20/2013, 11:56:56 AM Β· Difficulty 9.8615 Β· 6,643,460 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
5db223d1bb321b852a66e5b26d4a0d75438549c06c7c862f78dadaa064f1a94f
View on Chainz β†—

Height

#172,759

Difficulty

9.861545

Transactions

1

Size

199 B

Version

2

Bits

09dc8e32

Nonce

249,030

Timestamp

9/20/2013, 11:56:56 AM

Confirmations

6,643,460

Merkle Root

00607cc065e4b85617feecf3e922facdbea39b89147198a1fd68703e49d22423
Transactions (1)
Coinbase00607cc065e4b8…68703e49d22423
1 in β†’ 1 out10.2700 XPM109 B
AM1A9CZL…as4Lpogj
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.

4.685 Γ— 10⁹⁴(95-digit number)
46850357389104012854…83010725087738090720
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
4.685 Γ— 10⁹⁴(95-digit number)
46850357389104012854…83010725087738090719
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.685 Γ— 10⁹⁴(95-digit number)
46850357389104012854…83010725087738090721
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
9.370 Γ— 10⁹⁴(95-digit number)
93700714778208025709…66021450175476181439
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
9.370 Γ— 10⁹⁴(95-digit number)
93700714778208025709…66021450175476181441
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
1.874 Γ— 10⁹⁡(96-digit number)
18740142955641605141…32042900350952362879
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.874 Γ— 10⁹⁡(96-digit number)
18740142955641605141…32042900350952362881
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
3.748 Γ— 10⁹⁡(96-digit number)
37480285911283210283…64085800701904725759
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.748 Γ— 10⁹⁡(96-digit number)
37480285911283210283…64085800701904725761
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
7.496 Γ— 10⁹⁡(96-digit number)
74960571822566420567…28171601403809451519
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 172759

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 5db223d1bb321b852a66e5b26d4a0d75438549c06c7c862f78dadaa064f1a94f

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 #172,759 on Chainz β†—
Circulating Supply:57,773,881 XPMΒ·at block #6,816,218 Β· updates every 60s
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