XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #377,384

Block #377,384

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 1/27/2014, 2:09:24 AM Β· Difficulty 10.4218 Β· 6,453,164 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
3e5b66101f9fd65f73af5a2fe0c9c77847eb5fdfe009bf071454e4a253b4b3dc
View on Chainz β†—

Height

#377,384

Difficulty

10.421754

Transactions

2

Size

720 B

Version

2

Bits

0a6bf814

Nonce

39,542

Timestamp

1/27/2014, 2:09:24 AM

Confirmations

6,453,164

Merkle Root

9372922768d469142729272f22ecdbb78ce115ad917858050ca24c3f379090f2
Transactions (2)
Coinbase171e872f750b22…1afe40bdf8ab72
1 in β†’ 1 out9.2000 XPM109 B
AQmkJXQb…gMKzNKig
d462a8058a9612…d18b18a9adc60d
3 in β†’ 2 out2.9126 XPM521 B
AHF8XA69…dFDtFuyFAGAQma9A…AW8JPSw5
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.

9.879 Γ— 10⁹³(94-digit number)
98794876875047562989…46366179163130966000
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
9.879 Γ— 10⁹³(94-digit number)
98794876875047562989…46366179163130965999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
9.879 Γ— 10⁹³(94-digit number)
98794876875047562989…46366179163130966001
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
1.975 Γ— 10⁹⁴(95-digit number)
19758975375009512597…92732358326261931999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.975 Γ— 10⁹⁴(95-digit number)
19758975375009512597…92732358326261932001
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
3.951 Γ— 10⁹⁴(95-digit number)
39517950750019025195…85464716652523863999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.951 Γ— 10⁹⁴(95-digit number)
39517950750019025195…85464716652523864001
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
7.903 Γ— 10⁹⁴(95-digit number)
79035901500038050391…70929433305047727999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
7.903 Γ— 10⁹⁴(95-digit number)
79035901500038050391…70929433305047728001
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
1.580 Γ— 10⁹⁡(96-digit number)
15807180300007610078…41858866610095455999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.580 Γ— 10⁹⁡(96-digit number)
15807180300007610078…41858866610095456001
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 377384

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 3e5b66101f9fd65f73af5a2fe0c9c77847eb5fdfe009bf071454e4a253b4b3dc

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 #377,384 on Chainz β†—
Circulating Supply:57,888,542 XPMΒ·at block #6,830,547 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