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Home/Chain Registry/Block #3,130,802

Block #3,130,802

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 4/8/2019, 8:59:07 PM Β· Difficulty 11.3104 Β· 3,712,509 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
d9c543eebcf483f1a505f71dc00e11a086d89ae4306d8c30c4f3d290a9f7b53b
View on Chainz β†—

Difficulty

11.310420

Transactions

1

Size

200 B

Version

2

Bits

0b4f77b1

Nonce

973,720,106

Timestamp

4/8/2019, 8:59:07 PM

Confirmations

3,712,509

Merkle Root

83b1ae78b223a7a43c8497c28139eacef7d122a4a06e71dc35c4fd8dcd087274
Transactions (1)
Coinbase83b1ae78b223a7…c4fd8dcd087274
1 in β†’ 1 out7.8000 XPM110 B
AbXwmGxD…4XXYP765
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.

2.347 Γ— 10⁹⁡(96-digit number)
23476047318131808273…52530293149758832640
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
2.347 Γ— 10⁹⁡(96-digit number)
23476047318131808273…52530293149758832639
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.347 Γ— 10⁹⁡(96-digit number)
23476047318131808273…52530293149758832641
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
4.695 Γ— 10⁹⁡(96-digit number)
46952094636263616546…05060586299517665279
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.695 Γ— 10⁹⁡(96-digit number)
46952094636263616546…05060586299517665281
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
9.390 Γ— 10⁹⁡(96-digit number)
93904189272527233093…10121172599035330559
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
9.390 Γ— 10⁹⁡(96-digit number)
93904189272527233093…10121172599035330561
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
1.878 Γ— 10⁹⁢(97-digit number)
18780837854505446618…20242345198070661119
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.878 Γ— 10⁹⁢(97-digit number)
18780837854505446618…20242345198070661121
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
3.756 Γ— 10⁹⁢(97-digit number)
37561675709010893237…40484690396141322239
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.756 Γ— 10⁹⁢(97-digit number)
37561675709010893237…40484690396141322241
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
7.512 Γ— 10⁹⁢(97-digit number)
75123351418021786474…80969380792282644479
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 3130802

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 d9c543eebcf483f1a505f71dc00e11a086d89ae4306d8c30c4f3d290a9f7b53b

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 #3,130,802 on Chainz β†—
Circulating Supply:57,990,855 XPMΒ·at block #6,843,310 Β· updates every 60s
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