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Home/Chain Registry/Block #1,414,822

Block #1,414,822

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 1/15/2016, 9:06:17 PM Β· Difficulty 10.7983 Β· 5,418,493 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
9a16e32fbf40bc7dd4431753a7f300bb0ed0883d9f39d576958d2081f2536af0
View on Chainz β†—

Difficulty

10.798299

Transactions

1

Size

201 B

Version

2

Bits

0acc5d58

Nonce

206,946,537

Timestamp

1/15/2016, 9:06:17 PM

Confirmations

5,418,493

Merkle Root

6b7e91f4bc823e1bcd5de2a81fab58c475a11287db88943117137a9ff2a60f68
Transactions (1)
Coinbase6b7e91f4bc823e…137a9ff2a60f68
1 in β†’ 1 out8.5600 XPM110 B
AaosZtLW…M6rDBDNp
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.

5.612 Γ— 10⁹⁷(98-digit number)
56123374157581564504…77372422901509980160
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
5.612 Γ— 10⁹⁷(98-digit number)
56123374157581564504…77372422901509980159
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.612 Γ— 10⁹⁷(98-digit number)
56123374157581564504…77372422901509980161
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
1.122 Γ— 10⁹⁸(99-digit number)
11224674831516312900…54744845803019960319
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.122 Γ— 10⁹⁸(99-digit number)
11224674831516312900…54744845803019960321
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
2.244 Γ— 10⁹⁸(99-digit number)
22449349663032625801…09489691606039920639
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.244 Γ— 10⁹⁸(99-digit number)
22449349663032625801…09489691606039920641
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
4.489 Γ— 10⁹⁸(99-digit number)
44898699326065251603…18979383212079841279
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.489 Γ— 10⁹⁸(99-digit number)
44898699326065251603…18979383212079841281
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
8.979 Γ— 10⁹⁸(99-digit number)
89797398652130503207…37958766424159682559
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
8.979 Γ— 10⁹⁸(99-digit number)
89797398652130503207…37958766424159682561
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
1.795 Γ— 10⁹⁹(100-digit number)
17959479730426100641…75917532848319365119
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 1414822

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 9a16e32fbf40bc7dd4431753a7f300bb0ed0883d9f39d576958d2081f2536af0

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 #1,414,822 on Chainz β†—
Circulating Supply:57,910,711 XPMΒ·at block #6,833,314 Β· updates every 60s
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