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Home/Chain Registry/Block #3,373,849

Block #3,373,849

TWNLength 12β˜…β˜…β˜…β˜…β˜†

Bi-Twin Chain Β· Discovered 9/29/2019, 9:06:43 AM Β· Difficulty 10.9947 Β· 3,467,185 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
0adf2c758b2766731ee8f4d0e7ab1366c60e6c647fd745d263e50fb2284a5221
View on Chainz β†—

Difficulty

10.994713

Transactions

1

Size

200 B

Version

2

Bits

0afea589

Nonce

190,036,932

Timestamp

9/29/2019, 9:06:43 AM

Confirmations

3,467,185

Merkle Root

9cfa76ad9b1314382cc61b9c2a719d04dcab2669fa8625f2c18d749b970e3d39
Transactions (1)
Coinbase9cfa76ad9b1314…8d749b970e3d39
1 in β†’ 1 out8.2600 XPM110 B
ASiq2qtK…VMhmk7yL
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.

1.780 Γ— 10⁹⁡(96-digit number)
17800191568092930562…74180260627316011200
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
1.780 Γ— 10⁹⁡(96-digit number)
17800191568092930562…74180260627316011199
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.780 Γ— 10⁹⁡(96-digit number)
17800191568092930562…74180260627316011201
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
3.560 Γ— 10⁹⁡(96-digit number)
35600383136185861125…48360521254632022399
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.560 Γ— 10⁹⁡(96-digit number)
35600383136185861125…48360521254632022401
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
7.120 Γ— 10⁹⁡(96-digit number)
71200766272371722251…96721042509264044799
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
7.120 Γ— 10⁹⁡(96-digit number)
71200766272371722251…96721042509264044801
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
1.424 Γ— 10⁹⁢(97-digit number)
14240153254474344450…93442085018528089599
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.424 Γ— 10⁹⁢(97-digit number)
14240153254474344450…93442085018528089601
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
2.848 Γ— 10⁹⁢(97-digit number)
28480306508948688900…86884170037056179199
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.848 Γ— 10⁹⁢(97-digit number)
28480306508948688900…86884170037056179201
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
5.696 Γ— 10⁹⁢(97-digit number)
56960613017897377801…73768340074112358399
Verify on FactorDB β†—Wolfram Alpha β†—
2^5 Γ— origin + 1
5.696 Γ— 10⁹⁢(97-digit number)
56960613017897377801…73768340074112358401
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^5 Γ— origin + 1 βˆ’ 2^5 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 12 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
ExceptionalChain length 12
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 3373849

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 0adf2c758b2766731ee8f4d0e7ab1366c60e6c647fd745d263e50fb2284a5221

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 #3,373,849 on Chainz β†—
Circulating Supply:57,972,631 XPMΒ·at block #6,841,033 Β· updates every 60s
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