XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #2,813,976

Block #2,813,976

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 8/28/2018, 3:40:51 PM Β· Difficulty 11.6790 Β· 4,028,386 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
79b16c25efa3298f2b662e7e21b2190ccb27756adf6c366176279f136e2f5e94
View on Chainz β†—

Difficulty

11.679034

Transactions

2

Size

688 B

Version

2

Bits

0badd52a

Nonce

529,581,978

Timestamp

8/28/2018, 3:40:51 PM

Confirmations

4,028,386

Merkle Root

f3eb3e679963c6cb7b7ccfcc6ab544a7dfa0f63417e69d49db2784310212cac1
Transactions (2)
Coinbasec3d2740de0161f…74baf4e766fb93
1 in β†’ 1 out7.3300 XPM110 B
APuCRnfT…HF6DBgCu
c17546681ab538…c6f1ab132fc335
3 in β†’ 1 out800.0000 XPM488 B
AKT2tLH9…dX1nXtTS
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.

2.428 Γ— 10⁹³(94-digit number)
24287800860713513193…22839025374057167910
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
2.428 Γ— 10⁹³(94-digit number)
24287800860713513193…22839025374057167909
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.428 Γ— 10⁹³(94-digit number)
24287800860713513193…22839025374057167911
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
4.857 Γ— 10⁹³(94-digit number)
48575601721427026387…45678050748114335819
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.857 Γ— 10⁹³(94-digit number)
48575601721427026387…45678050748114335821
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
9.715 Γ— 10⁹³(94-digit number)
97151203442854052774…91356101496228671639
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
9.715 Γ— 10⁹³(94-digit number)
97151203442854052774…91356101496228671641
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
1.943 Γ— 10⁹⁴(95-digit number)
19430240688570810554…82712202992457343279
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.943 Γ— 10⁹⁴(95-digit number)
19430240688570810554…82712202992457343281
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
3.886 Γ— 10⁹⁴(95-digit number)
38860481377141621109…65424405984914686559
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.886 Γ— 10⁹⁴(95-digit number)
38860481377141621109…65424405984914686561
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
7.772 Γ— 10⁹⁴(95-digit number)
77720962754283242219…30848811969829373119
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 2813976

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 79b16c25efa3298f2b662e7e21b2190ccb27756adf6c366176279f136e2f5e94

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 #2,813,976 on Chainz β†—
Circulating Supply:57,983,304 XPMΒ·at block #6,842,361 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