XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #320,786

Block #320,786

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 12/19/2013, 9:28:31 PM Β· Difficulty 10.1849 Β· 6,475,201 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
cea2111102ef3b466d81929eef69ab1909da33c182d27fdd37b130ce37fd62ad
View on Chainz β†—

Height

#320,786

Difficulty

10.184943

Transactions

1

Size

208 B

Version

2

Bits

0a2f5871

Nonce

13,243

Timestamp

12/19/2013, 9:28:31 PM

Confirmations

6,475,201

Merkle Root

1ac551ce50680af30b2d75f5e2671138226d9bfd5eb1dd824668168501acb6bd
Transactions (1)
Coinbase1ac551ce50680a…68168501acb6bd
1 in β†’ 1 out9.6300 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.

2.172 Γ— 10⁹⁸(99-digit number)
21727916037996841959…06271385519586196190
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
2.172 Γ— 10⁹⁸(99-digit number)
21727916037996841959…06271385519586196189
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.172 Γ— 10⁹⁸(99-digit number)
21727916037996841959…06271385519586196191
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
4.345 Γ— 10⁹⁸(99-digit number)
43455832075993683918…12542771039172392379
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.345 Γ— 10⁹⁸(99-digit number)
43455832075993683918…12542771039172392381
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
8.691 Γ— 10⁹⁸(99-digit number)
86911664151987367837…25085542078344784759
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
8.691 Γ— 10⁹⁸(99-digit number)
86911664151987367837…25085542078344784761
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
1.738 Γ— 10⁹⁹(100-digit number)
17382332830397473567…50171084156689569519
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.738 Γ— 10⁹⁹(100-digit number)
17382332830397473567…50171084156689569521
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
3.476 Γ— 10⁹⁹(100-digit number)
34764665660794947134…00342168313379139039
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.476 Γ— 10⁹⁹(100-digit number)
34764665660794947134…00342168313379139041
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
6.952 Γ— 10⁹⁹(100-digit number)
69529331321589894269…00684336626758278079
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11
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 320786

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 cea2111102ef3b466d81929eef69ab1909da33c182d27fdd37b130ce37fd62ad

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 #320,786 on Chainz β†—
Circulating Supply:57,611,991 XPMΒ·at block #6,795,986 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