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Home/Chain Registry/Block #1,627,833

Block #1,627,833

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 6/14/2016, 8:21:26 AM Β· Difficulty 10.5945 Β· 5,215,446 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
4cee8830b25a5610824744a6e2df1f34d0fda8958e16da0854abdc4321349e92
View on Chainz β†—

Difficulty

10.594476

Transactions

1

Size

199 B

Version

2

Bits

0a982f9b

Nonce

1,476,576,245

Timestamp

6/14/2016, 8:21:26 AM

Confirmations

5,215,446

Merkle Root

08428588c411371d99882b0f24093da777901e068476221bf75676c2c238da67
Transactions (1)
Coinbase08428588c41137…5676c2c238da67
1 in β†’ 1 out8.9000 XPM109 B
AaesaCrD…6oZkdCgd
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.

4.443 Γ— 10⁹⁴(95-digit number)
44436924431720041807…00889113907791162760
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
4.443 Γ— 10⁹⁴(95-digit number)
44436924431720041807…00889113907791162759
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.443 Γ— 10⁹⁴(95-digit number)
44436924431720041807…00889113907791162761
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
8.887 Γ— 10⁹⁴(95-digit number)
88873848863440083615…01778227815582325519
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
8.887 Γ— 10⁹⁴(95-digit number)
88873848863440083615…01778227815582325521
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
1.777 Γ— 10⁹⁡(96-digit number)
17774769772688016723…03556455631164651039
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.777 Γ— 10⁹⁡(96-digit number)
17774769772688016723…03556455631164651041
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
3.554 Γ— 10⁹⁡(96-digit number)
35549539545376033446…07112911262329302079
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.554 Γ— 10⁹⁡(96-digit number)
35549539545376033446…07112911262329302081
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
7.109 Γ— 10⁹⁡(96-digit number)
71099079090752066892…14225822524658604159
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
7.109 Γ— 10⁹⁡(96-digit number)
71099079090752066892…14225822524658604161
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 1627833

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 4cee8830b25a5610824744a6e2df1f34d0fda8958e16da0854abdc4321349e92

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 #1,627,833 on Chainz β†—
Circulating Supply:57,990,608 XPMΒ·at block #6,843,278 Β· updates every 60s
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