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Block #3,243,413

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 6/27/2019, 4:17:13 PM Β· Difficulty 11.0012 Β· 3,597,207 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
53f708ec173f4fc86281b01f1c587cc8cde71029e99932d85a96df2c8db25f9e
View on Chainz β†—

Difficulty

11.001172

Transactions

1

Size

201 B

Version

2

Bits

0b004cd0

Nonce

410,797,324

Timestamp

6/27/2019, 4:17:13 PM

Confirmations

3,597,207

Merkle Root

96fba78a58bec599c6436a4c97e2572bf65f2ee622f3fb85e99eca31beba51fa
Transactions (1)
Coinbase96fba78a58bec5…9eca31beba51fa
1 in β†’ 1 out8.2500 XPM110 B
ARbm48qR…9xQc8DBX
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.

2.932 Γ— 10⁹⁢(97-digit number)
29327804193751123861…32636291956820943360
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
2.932 Γ— 10⁹⁢(97-digit number)
29327804193751123861…32636291956820943359
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.932 Γ— 10⁹⁢(97-digit number)
29327804193751123861…32636291956820943361
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
5.865 Γ— 10⁹⁢(97-digit number)
58655608387502247722…65272583913641886719
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.865 Γ— 10⁹⁢(97-digit number)
58655608387502247722…65272583913641886721
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
1.173 Γ— 10⁹⁷(98-digit number)
11731121677500449544…30545167827283773439
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.173 Γ— 10⁹⁷(98-digit number)
11731121677500449544…30545167827283773441
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
2.346 Γ— 10⁹⁷(98-digit number)
23462243355000899089…61090335654567546879
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.346 Γ— 10⁹⁷(98-digit number)
23462243355000899089…61090335654567546881
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
4.692 Γ— 10⁹⁷(98-digit number)
46924486710001798178…22180671309135093759
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.692 Γ— 10⁹⁷(98-digit number)
46924486710001798178…22180671309135093761
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
9.384 Γ— 10⁹⁷(98-digit number)
93848973420003596356…44361342618270187519
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 3243413

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 53f708ec173f4fc86281b01f1c587cc8cde71029e99932d85a96df2c8db25f9e

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 #3,243,413 on Chainz β†—
Circulating Supply:57,969,299 XPMΒ·at block #6,840,619 Β· updates every 60s
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