XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #341,105

Block #341,105

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 1/3/2014, 6:12:19 AM Β· Difficulty 10.1314 Β· 6,472,767 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
7624d58dba4c2ce113d53fcb16328e87a3b67f9ad0ea4d2fd3d63c0a26494b7d
View on Chainz β†—

Height

#341,105

Difficulty

10.131401

Transactions

3

Size

766 B

Version

2

Bits

0a21a379

Nonce

35,858

Timestamp

1/3/2014, 6:12:19 AM

Confirmations

6,472,767

Merkle Root

d555b0d01118753c8cf8c6c81bad445cc53ed41a5154740c62b9ecb8ce0db836
Transactions (3)
Coinbasea9271ee7885983…731e4a5885c340
1 in β†’ 1 out9.7500 XPM109 B
AYEzJq7k…7DzDky4R
06b9790565e85f…b4bf6695bb0a48
1 in β†’ 1 out2.9914 XPM191 B
AS3g1UmJ…AAKgQ8CW
810036984a52fb…4ea4e5f2059600
2 in β†’ 2 out1.1249 XPM375 B
AQcv3kkp…nfY46tWYAKBityws…1GAbJmiE
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.

2.056 Γ— 10⁹⁷(98-digit number)
20568835591368447101…82632938600924998400
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
2.056 Γ— 10⁹⁷(98-digit number)
20568835591368447101…82632938600924998399
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.056 Γ— 10⁹⁷(98-digit number)
20568835591368447101…82632938600924998401
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
4.113 Γ— 10⁹⁷(98-digit number)
41137671182736894202…65265877201849996799
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.113 Γ— 10⁹⁷(98-digit number)
41137671182736894202…65265877201849996801
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
8.227 Γ— 10⁹⁷(98-digit number)
82275342365473788404…30531754403699993599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
8.227 Γ— 10⁹⁷(98-digit number)
82275342365473788404…30531754403699993601
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
1.645 Γ— 10⁹⁸(99-digit number)
16455068473094757680…61063508807399987199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.645 Γ— 10⁹⁸(99-digit number)
16455068473094757680…61063508807399987201
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
3.291 Γ— 10⁹⁸(99-digit number)
32910136946189515361…22127017614799974399
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.291 Γ— 10⁹⁸(99-digit number)
32910136946189515361…22127017614799974401
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 341105

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 7624d58dba4c2ce113d53fcb16328e87a3b67f9ad0ea4d2fd3d63c0a26494b7d

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 #341,105 on Chainz β†—
Circulating Supply:57,755,050 XPMΒ·at block #6,813,871 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