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Home/Chain Registry/Block #3,242,597

Block #3,242,597

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 6/27/2019, 2:31:20 AM Β· Difficulty 11.0027 Β· 3,591,144 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
82e1e20ec1c46a5ac4ffc754276111bc2ea2777fed7ed20b5d857808d0b5d3c7
View on Chainz β†—

Difficulty

11.002690

Transactions

2

Size

8.21 KB

Version

2

Bits

0b00b047

Nonce

906,654,675

Timestamp

6/27/2019, 2:31:20 AM

Confirmations

3,591,144

Merkle Root

3249e1382e769b824d9fc83cf475629b2eda8cafbb1e31968708782fbf035f51
Transactions (2)
Coinbase23b8af02333b07…aaeea01e539f03
1 in β†’ 1 out8.3400 XPM110 B
ARbm48qR…9xQc8DBX
a91f91367fb3f0…011c03c6706d8d
55 in β†’ 2 out1773.0334 XPM8.02 KB
AVDvwh2P…b6H33JtEANcE4iqA…f6KLuoPQ
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.

3.255 Γ— 10⁹⁷(98-digit number)
32551112620615682500…90053790801578803200
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
3.255 Γ— 10⁹⁷(98-digit number)
32551112620615682500…90053790801578803199
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.255 Γ— 10⁹⁷(98-digit number)
32551112620615682500…90053790801578803201
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
6.510 Γ— 10⁹⁷(98-digit number)
65102225241231365001…80107581603157606399
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.510 Γ— 10⁹⁷(98-digit number)
65102225241231365001…80107581603157606401
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
1.302 Γ— 10⁹⁸(99-digit number)
13020445048246273000…60215163206315212799
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.302 Γ— 10⁹⁸(99-digit number)
13020445048246273000…60215163206315212801
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
2.604 Γ— 10⁹⁸(99-digit number)
26040890096492546000…20430326412630425599
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.604 Γ— 10⁹⁸(99-digit number)
26040890096492546000…20430326412630425601
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
5.208 Γ— 10⁹⁸(99-digit number)
52081780192985092000…40860652825260851199
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.208 Γ— 10⁹⁸(99-digit number)
52081780192985092000…40860652825260851201
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
1.041 Γ— 10⁹⁹(100-digit number)
10416356038597018400…81721305650521702399
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 3242597

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 82e1e20ec1c46a5ac4ffc754276111bc2ea2777fed7ed20b5d857808d0b5d3c7

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 #3,242,597 on Chainz β†—
Circulating Supply:57,914,146 XPMΒ·at block #6,833,740 Β· updates every 60s
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