XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #2,699,724

Block #2,699,724

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 6/10/2018, 3:39:48 PM Β· Difficulty 11.6422 Β· 4,145,507 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
194fe1ccaabf8454ce9927737867cc9cf9bfaa82f2b171eeddb1f957d1bb1317
View on Chainz β†—

Difficulty

11.642217

Transactions

1

Size

200 B

Version

2

Bits

0ba46857

Nonce

1,438,527,445

Timestamp

6/10/2018, 3:39:48 PM

Confirmations

4,145,507

Merkle Root

1d440cdc4e608004db6265bb23e09afe257019fe05f2d2f8a4a6e81daa4a1b98
Transactions (1)
Coinbase1d440cdc4e6080…a6e81daa4a1b98
1 in β†’ 1 out7.3700 XPM110 B
AZtxQr2F…7grUWrUz
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.

1.660 Γ— 10⁹⁡(96-digit number)
16603293597833564822…94887659019436903860
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
1.660 Γ— 10⁹⁡(96-digit number)
16603293597833564822…94887659019436903859
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.660 Γ— 10⁹⁡(96-digit number)
16603293597833564822…94887659019436903861
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
3.320 Γ— 10⁹⁡(96-digit number)
33206587195667129645…89775318038873807719
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.320 Γ— 10⁹⁡(96-digit number)
33206587195667129645…89775318038873807721
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
6.641 Γ— 10⁹⁡(96-digit number)
66413174391334259291…79550636077747615439
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.641 Γ— 10⁹⁡(96-digit number)
66413174391334259291…79550636077747615441
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
1.328 Γ— 10⁹⁢(97-digit number)
13282634878266851858…59101272155495230879
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.328 Γ— 10⁹⁢(97-digit number)
13282634878266851858…59101272155495230881
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
2.656 Γ— 10⁹⁢(97-digit number)
26565269756533703716…18202544310990461759
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.656 Γ— 10⁹⁢(97-digit number)
26565269756533703716…18202544310990461761
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
5.313 Γ— 10⁹⁢(97-digit number)
53130539513067407433…36405088621980923519
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 2699724

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 194fe1ccaabf8454ce9927737867cc9cf9bfaa82f2b171eeddb1f957d1bb1317

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 #2,699,724 on Chainz β†—
Circulating Supply:58,006,279 XPMΒ·at block #6,845,230 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