XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #393,151

Block #393,151

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 2/6/2014, 10:33:53 PM Β· Difficulty 10.4430 Β· 6,401,462 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
d09ee54e88a69ca2b3d9b21fbd0646a91fe03151448d94349c918b1f7490c06a
View on Chainz β†—

Height

#393,151

Difficulty

10.443017

Transactions

1

Size

207 B

Version

2

Bits

0a716996

Nonce

26,718

Timestamp

2/6/2014, 10:33:53 PM

Confirmations

6,401,462

Merkle Root

d47e29853ff830dc6c1834cb5d31a0d231da8ab6d373050757cd2027a319ef95
Transactions (1)
Coinbased47e29853ff830…cd2027a319ef95
1 in β†’ 1 out9.1600 XPM116 B
AbwWkWZt…kawDhufa
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.

2.827 Γ— 10⁹⁷(98-digit number)
28275933214032215728…56398022379773528010
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
2.827 Γ— 10⁹⁷(98-digit number)
28275933214032215728…56398022379773528009
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.827 Γ— 10⁹⁷(98-digit number)
28275933214032215728…56398022379773528011
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
5.655 Γ— 10⁹⁷(98-digit number)
56551866428064431456…12796044759547056019
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.655 Γ— 10⁹⁷(98-digit number)
56551866428064431456…12796044759547056021
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
1.131 Γ— 10⁹⁸(99-digit number)
11310373285612886291…25592089519094112039
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.131 Γ— 10⁹⁸(99-digit number)
11310373285612886291…25592089519094112041
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
2.262 Γ— 10⁹⁸(99-digit number)
22620746571225772582…51184179038188224079
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.262 Γ— 10⁹⁸(99-digit number)
22620746571225772582…51184179038188224081
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
4.524 Γ— 10⁹⁸(99-digit number)
45241493142451545165…02368358076376448159
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.524 Γ— 10⁹⁸(99-digit number)
45241493142451545165…02368358076376448161
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 393151

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 d09ee54e88a69ca2b3d9b21fbd0646a91fe03151448d94349c918b1f7490c06a

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 #393,151 on Chainz β†—
Circulating Supply:57,600,947 XPMΒ·at block #6,794,612 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.
AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK