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Home/Chain Registry/Block #1,532,689

Block #1,532,689

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 4/9/2016, 1:28:24 AM Β· Difficulty 10.6143 Β· 5,312,465 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
a2c9c69182315daca1bbfd0f69f76185322da417c91a00fb8d167b2c698c61b9
View on Chainz β†—

Difficulty

10.614320

Transactions

1

Size

200 B

Version

2

Bits

0a9d441b

Nonce

800,882,251

Timestamp

4/9/2016, 1:28:24 AM

Confirmations

5,312,465

Merkle Root

eecfca63bb36d01be8e743cb0bea424f82d28d1b24f73c783ccb7212724369b4
Transactions (1)
Coinbaseeecfca63bb36d0…cb7212724369b4
1 in β†’ 1 out8.8600 XPM110 B
AHcfjaRH…aBvsbFZ8
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.

1.833 Γ— 10⁹⁡(96-digit number)
18330933187713108737…96509157803053948800
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
1.833 Γ— 10⁹⁡(96-digit number)
18330933187713108737…96509157803053948799
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.833 Γ— 10⁹⁡(96-digit number)
18330933187713108737…96509157803053948801
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
3.666 Γ— 10⁹⁡(96-digit number)
36661866375426217474…93018315606107897599
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.666 Γ— 10⁹⁡(96-digit number)
36661866375426217474…93018315606107897601
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
7.332 Γ— 10⁹⁡(96-digit number)
73323732750852434949…86036631212215795199
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
7.332 Γ— 10⁹⁡(96-digit number)
73323732750852434949…86036631212215795201
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
1.466 Γ— 10⁹⁢(97-digit number)
14664746550170486989…72073262424431590399
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.466 Γ— 10⁹⁢(97-digit number)
14664746550170486989…72073262424431590401
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
2.932 Γ— 10⁹⁢(97-digit number)
29329493100340973979…44146524848863180799
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.932 Γ— 10⁹⁢(97-digit number)
29329493100340973979…44146524848863180801
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 1532689

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 a2c9c69182315daca1bbfd0f69f76185322da417c91a00fb8d167b2c698c61b9

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 #1,532,689 on Chainz β†—
Circulating Supply:58,005,660 XPMΒ·at block #6,845,153 Β· updates every 60s
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