XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #336,659

Block #336,659

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 12/31/2013, 2:56:29 AM Β· Difficulty 10.1422 Β· 6,489,651 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
26487b303c8ff0a8c0c75495aa82a9c0bed2644a44e16c101cbc9d199b30ebd1
View on Chainz β†—

Height

#336,659

Difficulty

10.142170

Transactions

1

Size

206 B

Version

2

Bits

0a246546

Nonce

77,799

Timestamp

12/31/2013, 2:56:29 AM

Confirmations

6,489,651

Merkle Root

aa358fd0d02f09abcdecf83882c971541c6e956051f0fdc5401f4d139c640858
Transactions (1)
Coinbaseaa358fd0d02f09…1f4d139c640858
1 in β†’ 1 out9.7100 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.

2.259 Γ— 10⁹⁡(96-digit number)
22593197928543822286…54516620516598998220
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
2.259 Γ— 10⁹⁡(96-digit number)
22593197928543822286…54516620516598998219
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.259 Γ— 10⁹⁡(96-digit number)
22593197928543822286…54516620516598998221
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
4.518 Γ— 10⁹⁡(96-digit number)
45186395857087644573…09033241033197996439
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.518 Γ— 10⁹⁡(96-digit number)
45186395857087644573…09033241033197996441
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
9.037 Γ— 10⁹⁡(96-digit number)
90372791714175289146…18066482066395992879
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
9.037 Γ— 10⁹⁡(96-digit number)
90372791714175289146…18066482066395992881
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
1.807 Γ— 10⁹⁢(97-digit number)
18074558342835057829…36132964132791985759
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.807 Γ— 10⁹⁢(97-digit number)
18074558342835057829…36132964132791985761
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
3.614 Γ— 10⁹⁢(97-digit number)
36149116685670115658…72265928265583971519
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.614 Γ— 10⁹⁢(97-digit number)
36149116685670115658…72265928265583971521
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10
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 336659

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 26487b303c8ff0a8c0c75495aa82a9c0bed2644a44e16c101cbc9d199b30ebd1

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 #336,659 on Chainz β†—
Circulating Supply:57,854,620 XPMΒ·at block #6,826,309 Β· updates every 60s
xpmprime.info is a work in progress. If you enjoy using this service you can support this project with a Primecoin donation.
Privacy PolicyΒ·
AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

Cookie Preferences

We use cookies to enhance your experience. Some are essential for the site to function, while others help us understand how you use the site.

Β·Privacy Policy