XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #3,503,560

Block #3,503,560

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 1/7/2020, 7:22:18 AM Β· Difficulty 10.9309 Β· 3,333,827 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
9ab22d124408dce44cf20b7e7f44299fe571f5b1c8fb4be2f39b9c1da99b7d80
View on Chainz β†—

Difficulty

10.930850

Transactions

1

Size

201 B

Version

2

Bits

0aee4c37

Nonce

1,886,835,570

Timestamp

1/7/2020, 7:22:18 AM

Confirmations

3,333,827

Merkle Root

e54b411ff79dd8241f8f302fcaae63541050cab4969d3e944f30e3490e7f1462
Transactions (1)
Coinbasee54b411ff79dd8…30e3490e7f1462
1 in β†’ 1 out8.3600 XPM110 B
ASiq2qtK…VMhmk7yL
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.

3.741 Γ— 10⁹⁷(98-digit number)
37416644171975246552…44343453486604042240
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
3.741 Γ— 10⁹⁷(98-digit number)
37416644171975246552…44343453486604042239
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.741 Γ— 10⁹⁷(98-digit number)
37416644171975246552…44343453486604042241
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
7.483 Γ— 10⁹⁷(98-digit number)
74833288343950493105…88686906973208084479
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
7.483 Γ— 10⁹⁷(98-digit number)
74833288343950493105…88686906973208084481
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
1.496 Γ— 10⁹⁸(99-digit number)
14966657668790098621…77373813946416168959
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.496 Γ— 10⁹⁸(99-digit number)
14966657668790098621…77373813946416168961
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
2.993 Γ— 10⁹⁸(99-digit number)
29933315337580197242…54747627892832337919
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.993 Γ— 10⁹⁸(99-digit number)
29933315337580197242…54747627892832337921
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
5.986 Γ— 10⁹⁸(99-digit number)
59866630675160394484…09495255785664675839
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.986 Γ— 10⁹⁸(99-digit number)
59866630675160394484…09495255785664675841
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 3503560

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 9ab22d124408dce44cf20b7e7f44299fe571f5b1c8fb4be2f39b9c1da99b7d80

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 #3,503,560 on Chainz β†—
Circulating Supply:57,943,419 XPMΒ·at block #6,837,386 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