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Home/Chain Registry/Block #1,534,576

Block #1,534,576

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 4/10/2016, 8:18:37 AM Β· Difficulty 10.6170 Β· 5,290,993 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
0d6909ceebbe01a4d330f778468e621eb5d2d4b4bb27d58c223f46af19e78c93
View on Chainz β†—

Difficulty

10.617042

Transactions

1

Size

199 B

Version

2

Bits

0a9df673

Nonce

1,293,280,506

Timestamp

4/10/2016, 8:18:37 AM

Confirmations

5,290,993

Merkle Root

43cba2b5599bac3f817fa1d1f1d16ecdbfaf0309cd012c737c29f3f7dfe70d31
Transactions (1)
Coinbase43cba2b5599bac…29f3f7dfe70d31
1 in β†’ 1 out8.8600 XPM109 B
AGcvAWWZ…d556fzZD
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.

1.924 Γ— 10⁹⁴(95-digit number)
19245515586714522909…01590210241994672500
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
1.924 Γ— 10⁹⁴(95-digit number)
19245515586714522909…01590210241994672499
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.924 Γ— 10⁹⁴(95-digit number)
19245515586714522909…01590210241994672501
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
3.849 Γ— 10⁹⁴(95-digit number)
38491031173429045818…03180420483989344999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.849 Γ— 10⁹⁴(95-digit number)
38491031173429045818…03180420483989345001
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
7.698 Γ— 10⁹⁴(95-digit number)
76982062346858091636…06360840967978689999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
7.698 Γ— 10⁹⁴(95-digit number)
76982062346858091636…06360840967978690001
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
1.539 Γ— 10⁹⁡(96-digit number)
15396412469371618327…12721681935957379999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.539 Γ— 10⁹⁡(96-digit number)
15396412469371618327…12721681935957380001
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
3.079 Γ— 10⁹⁡(96-digit number)
30792824938743236654…25443363871914759999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.079 Γ— 10⁹⁡(96-digit number)
30792824938743236654…25443363871914760001
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 1534576

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 0d6909ceebbe01a4d330f778468e621eb5d2d4b4bb27d58c223f46af19e78c93

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 #1,534,576 on Chainz β†—
Circulating Supply:57,848,654 XPMΒ·at block #6,825,568 Β· updates every 60s
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