XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #684,442

Block #684,442

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 8/19/2014, 10:29:10 PM Β· Difficulty 10.9578 Β· 6,142,922 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
2b3a08174cd298c5c033b7d57ce48ff63f7235443df36764801d37ace52e7154
View on Chainz β†—

Height

#684,442

Difficulty

10.957776

Transactions

2

Size

433 B

Version

2

Bits

0af530d7

Nonce

152,452,500

Timestamp

8/19/2014, 10:29:10 PM

Confirmations

6,142,922

Merkle Root

f521abb9a39d51324d0bfbbd99e283c7738ec2b57f6a6ae4712743001d7c59b9
Transactions (2)
Coinbasef8d150fc774b43…fed0af7893da59
1 in β†’ 1 out8.3200 XPM116 B
ANSXnLY2…Sd25TjkD
6311b54e6ddbe0…58c517eedf90e7
1 in β†’ 2 out8.2900 XPM226 B
AQAzxY74…NqbcivpHARSrvv1x…ZaaviNgn
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.

1.343 Γ— 10⁹⁷(98-digit number)
13435683448440812464…69049663566888576000
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
1.343 Γ— 10⁹⁷(98-digit number)
13435683448440812464…69049663566888575999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.343 Γ— 10⁹⁷(98-digit number)
13435683448440812464…69049663566888576001
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
2.687 Γ— 10⁹⁷(98-digit number)
26871366896881624928…38099327133777151999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.687 Γ— 10⁹⁷(98-digit number)
26871366896881624928…38099327133777152001
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
5.374 Γ— 10⁹⁷(98-digit number)
53742733793763249856…76198654267554303999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.374 Γ— 10⁹⁷(98-digit number)
53742733793763249856…76198654267554304001
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
1.074 Γ— 10⁹⁸(99-digit number)
10748546758752649971…52397308535108607999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.074 Γ— 10⁹⁸(99-digit number)
10748546758752649971…52397308535108608001
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
2.149 Γ— 10⁹⁸(99-digit number)
21497093517505299942…04794617070217215999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.149 Γ— 10⁹⁸(99-digit number)
21497093517505299942…04794617070217216001
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 684442

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 2b3a08174cd298c5c033b7d57ce48ff63f7235443df36764801d37ace52e7154

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 #684,442 on Chainz β†—
Circulating Supply:57,863,012 XPMΒ·at block #6,827,363 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