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Home/Chain Registry/Block #1,612,689

Block #1,612,689

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 6/3/2016, 6:22:09 PM Β· Difficulty 10.6013 Β· 5,230,220 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
86d4985d850dc8eca7eb172c75fe5796430fd10db34ea7d3ac8f33134c86762b
View on Chainz β†—

Difficulty

10.601259

Transactions

1

Size

199 B

Version

2

Bits

0a99ec15

Nonce

63,700,563

Timestamp

6/3/2016, 6:22:09 PM

Confirmations

5,230,220

Merkle Root

38ac7f99a10bf9f158b7e22afc7e852836209b48d68f2c663be9e8c25e59d8ec
Transactions (1)
Coinbase38ac7f99a10bf9…e9e8c25e59d8ec
1 in β†’ 1 out8.8800 XPM109 B
ALiiXhmR…Y81UhLzT
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.

8.895 Γ— 10⁹⁴(95-digit number)
88959660973982075143…56388380352346312000
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
8.895 Γ— 10⁹⁴(95-digit number)
88959660973982075143…56388380352346311999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
8.895 Γ— 10⁹⁴(95-digit number)
88959660973982075143…56388380352346312001
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
1.779 Γ— 10⁹⁡(96-digit number)
17791932194796415028…12776760704692623999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.779 Γ— 10⁹⁡(96-digit number)
17791932194796415028…12776760704692624001
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
3.558 Γ— 10⁹⁡(96-digit number)
35583864389592830057…25553521409385247999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.558 Γ— 10⁹⁡(96-digit number)
35583864389592830057…25553521409385248001
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
7.116 Γ— 10⁹⁡(96-digit number)
71167728779185660114…51107042818770495999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
7.116 Γ— 10⁹⁡(96-digit number)
71167728779185660114…51107042818770496001
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
1.423 Γ— 10⁹⁢(97-digit number)
14233545755837132022…02214085637540991999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.423 Γ— 10⁹⁢(97-digit number)
14233545755837132022…02214085637540992001
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 1612689

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 86d4985d850dc8eca7eb172c75fe5796430fd10db34ea7d3ac8f33134c86762b

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 #1,612,689 on Chainz β†—
Circulating Supply:57,987,619 XPMΒ·at block #6,842,908 Β· updates every 60s
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