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Block #305,170

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 12/11/2013, 8:22:40 AM Β· Difficulty 9.9935 Β· 6,537,125 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
f608179e8dbfb4b8633ecce36f366666db7ae93fd09fa926c039e64b8fb31403
View on Chainz β†—

Height

#305,170

Difficulty

9.993529

Transactions

1

Size

207 B

Version

2

Bits

09fe57ef

Nonce

31,278

Timestamp

12/11/2013, 8:22:40 AM

Confirmations

6,537,125

Merkle Root

058469ff0d6bf58aa21c1e951d991b27ea6f1d06e14dda913e0988c114a13952
Transactions (1)
Coinbase058469ff0d6bf5…0988c114a13952
1 in β†’ 1 out10.0000 XPM116 B
AbwWkWZt…kawDhufa
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.

2.129 Γ— 10⁹⁢(97-digit number)
21294744197958477450…95369431330119000840
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
2.129 Γ— 10⁹⁢(97-digit number)
21294744197958477450…95369431330119000839
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.129 Γ— 10⁹⁢(97-digit number)
21294744197958477450…95369431330119000841
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
4.258 Γ— 10⁹⁢(97-digit number)
42589488395916954901…90738862660238001679
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.258 Γ— 10⁹⁢(97-digit number)
42589488395916954901…90738862660238001681
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
8.517 Γ— 10⁹⁢(97-digit number)
85178976791833909802…81477725320476003359
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
8.517 Γ— 10⁹⁢(97-digit number)
85178976791833909802…81477725320476003361
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
1.703 Γ— 10⁹⁷(98-digit number)
17035795358366781960…62955450640952006719
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.703 Γ— 10⁹⁷(98-digit number)
17035795358366781960…62955450640952006721
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
3.407 Γ— 10⁹⁷(98-digit number)
34071590716733563921…25910901281904013439
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 305170

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 f608179e8dbfb4b8633ecce36f366666db7ae93fd09fa926c039e64b8fb31403

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 #305,170 on Chainz β†—
Circulating Supply:57,982,763 XPMΒ·at block #6,842,294 Β· updates every 60s
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