XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #419,706

Block #419,706

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 2/25/2014, 9:24:33 PM Β· Difficulty 10.3690 Β· 6,410,953 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
d04aae178801db278f4cb6cede863db3e96c3289d7697fa5f33293735a906ac5
View on Chainz β†—

Height

#419,706

Difficulty

10.369017

Transactions

1

Size

223 B

Version

2

Bits

0a5e77e0

Nonce

164,973

Timestamp

2/25/2014, 9:24:33 PM

Confirmations

6,410,953

Merkle Root

eb6e04fa2e83c30eddbdfc5644e9b16d3a1cb8739314bf7f24753663fc9bea01
Transactions (1)
Coinbaseeb6e04fa2e83c3…753663fc9bea01
1 in β†’ 2 out9.2900 XPM131 B
AMVf7Jrg…xd5AVR7CAJno7LX2…vo4wdWtY
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.

2.345 Γ— 10¹⁰⁰(101-digit number)
23451808711623009260…42486260153593960960
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
2.345 Γ— 10¹⁰⁰(101-digit number)
23451808711623009260…42486260153593960959
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.345 Γ— 10¹⁰⁰(101-digit number)
23451808711623009260…42486260153593960961
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
4.690 Γ— 10¹⁰⁰(101-digit number)
46903617423246018521…84972520307187921919
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.690 Γ— 10¹⁰⁰(101-digit number)
46903617423246018521…84972520307187921921
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
9.380 Γ— 10¹⁰⁰(101-digit number)
93807234846492037043…69945040614375843839
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
9.380 Γ— 10¹⁰⁰(101-digit number)
93807234846492037043…69945040614375843841
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
1.876 Γ— 10¹⁰¹(102-digit number)
18761446969298407408…39890081228751687679
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.876 Γ— 10¹⁰¹(102-digit number)
18761446969298407408…39890081228751687681
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
3.752 Γ— 10¹⁰¹(102-digit number)
37522893938596814817…79780162457503375359
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.752 Γ— 10¹⁰¹(102-digit number)
37522893938596814817…79780162457503375361
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 419706

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 d04aae178801db278f4cb6cede863db3e96c3289d7697fa5f33293735a906ac5

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 #419,706 on Chainz β†—
Circulating Supply:57,889,399 XPMΒ·at block #6,830,658 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