XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #1,679,422

Block #1,679,422

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/19/2016, 3:23:37 AM Β· Difficulty 10.7002 Β· 5,151,427 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
cd1a1b84b7c127ae66fa5a2d30bcd06234dab590278a2a5d3d5600f2bd0ec0c5
View on Chainz β†—

Difficulty

10.700237

Transactions

1

Size

244 B

Version

2

Bits

0ab342bb

Nonce

655,181,975

Timestamp

7/19/2016, 3:23:37 AM

Confirmations

5,151,427

Merkle Root

bb1d7543d2d6573fb7ea4ae450a03a60552592c9fb623e6d3a7d7d0e3548412d
Transactions (1)
Coinbasebb1d7543d2d657…7d7d0e3548412d
1 in β†’ 2 out8.7200 XPM152 B
AXyURe5W…4RkBkCpGALPu3s2c…EJXLjVFh
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.

3.023 Γ— 10⁹⁸(99-digit number)
30233015700846744926…90389717685372354560
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
3.023 Γ— 10⁹⁸(99-digit number)
30233015700846744926…90389717685372354559
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.023 Γ— 10⁹⁸(99-digit number)
30233015700846744926…90389717685372354561
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
6.046 Γ— 10⁹⁸(99-digit number)
60466031401693489853…80779435370744709119
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.046 Γ— 10⁹⁸(99-digit number)
60466031401693489853…80779435370744709121
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
1.209 Γ— 10⁹⁹(100-digit number)
12093206280338697970…61558870741489418239
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.209 Γ— 10⁹⁹(100-digit number)
12093206280338697970…61558870741489418241
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
2.418 Γ— 10⁹⁹(100-digit number)
24186412560677395941…23117741482978836479
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.418 Γ— 10⁹⁹(100-digit number)
24186412560677395941…23117741482978836481
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
4.837 Γ— 10⁹⁹(100-digit number)
48372825121354791882…46235482965957672959
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.837 Γ— 10⁹⁹(100-digit number)
48372825121354791882…46235482965957672961
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 1679422

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 cd1a1b84b7c127ae66fa5a2d30bcd06234dab590278a2a5d3d5600f2bd0ec0c5

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 #1,679,422 on Chainz β†—
Circulating Supply:57,890,927 XPMΒ·at block #6,830,848 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