XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #2,306,860

Block #2,306,860

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 9/24/2017, 4:14:23 AM Β· Difficulty 10.9120 Β· 4,527,004 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
dea23bbfe11770c5537b42bdd802394111123f1a425bf19ffc400d2ce5501f1c
View on Chainz β†—

Difficulty

10.912001

Transactions

1

Size

200 B

Version

2

Bits

0ae978e0

Nonce

478,411,222

Timestamp

9/24/2017, 4:14:23 AM

Confirmations

4,527,004

Merkle Root

414bb22cc10b77b37c4cc8c11927651e4ef741eb35fec403bdbe1a09cc34e313
Transactions (1)
Coinbase414bb22cc10b77…be1a09cc34e313
1 in β†’ 1 out8.3800 XPM110 B
AML6bhZ3…ZFCuy7kK
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.

9.928 Γ— 10⁹³(94-digit number)
99286257018128178867…06270655335291759360
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
9.928 Γ— 10⁹³(94-digit number)
99286257018128178867…06270655335291759359
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
9.928 Γ— 10⁹³(94-digit number)
99286257018128178867…06270655335291759361
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
1.985 Γ— 10⁹⁴(95-digit number)
19857251403625635773…12541310670583518719
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.985 Γ— 10⁹⁴(95-digit number)
19857251403625635773…12541310670583518721
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
3.971 Γ— 10⁹⁴(95-digit number)
39714502807251271547…25082621341167037439
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.971 Γ— 10⁹⁴(95-digit number)
39714502807251271547…25082621341167037441
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
7.942 Γ— 10⁹⁴(95-digit number)
79429005614502543094…50165242682334074879
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
7.942 Γ— 10⁹⁴(95-digit number)
79429005614502543094…50165242682334074881
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
1.588 Γ— 10⁹⁡(96-digit number)
15885801122900508618…00330485364668149759
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.588 Γ— 10⁹⁡(96-digit number)
15885801122900508618…00330485364668149761
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
3.177 Γ— 10⁹⁡(96-digit number)
31771602245801017237…00660970729336299519
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11
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 2306860

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 dea23bbfe11770c5537b42bdd802394111123f1a425bf19ffc400d2ce5501f1c

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 #2,306,860 on Chainz β†—
Circulating Supply:57,915,142 XPMΒ·at block #6,833,863 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