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Home/Chain Registry/Block #3,021,502

Block #3,021,502

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 1/23/2019, 3:44:53 AM Β· Difficulty 11.1694 Β· 3,823,690 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
3df0c2ab877ca5343b61ff570cd2660e56bf9d92e044c24586b52cbab09198ab
View on Chainz β†—

Difficulty

11.169416

Transactions

1

Size

200 B

Version

2

Bits

0b2b5ed8

Nonce

184,407,605

Timestamp

1/23/2019, 3:44:53 AM

Confirmations

3,823,690

Merkle Root

fa592ee77f2d63d3a47a3991693b4d4e9136505ae8447ddad8c02c936e76f7b6
Transactions (1)
Coinbasefa592ee77f2d63…c02c936e76f7b6
1 in β†’ 1 out8.0000 XPM110 B
AUhjokok…k5m93PZR
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.

2.268 Γ— 10⁹⁡(96-digit number)
22680947590699696567…00651380398736854880
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
2.268 Γ— 10⁹⁡(96-digit number)
22680947590699696567…00651380398736854879
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.268 Γ— 10⁹⁡(96-digit number)
22680947590699696567…00651380398736854881
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
4.536 Γ— 10⁹⁡(96-digit number)
45361895181399393134…01302760797473709759
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.536 Γ— 10⁹⁡(96-digit number)
45361895181399393134…01302760797473709761
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
9.072 Γ— 10⁹⁡(96-digit number)
90723790362798786269…02605521594947419519
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
9.072 Γ— 10⁹⁡(96-digit number)
90723790362798786269…02605521594947419521
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
1.814 Γ— 10⁹⁢(97-digit number)
18144758072559757253…05211043189894839039
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.814 Γ— 10⁹⁢(97-digit number)
18144758072559757253…05211043189894839041
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
3.628 Γ— 10⁹⁢(97-digit number)
36289516145119514507…10422086379789678079
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.628 Γ— 10⁹⁢(97-digit number)
36289516145119514507…10422086379789678081
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
7.257 Γ— 10⁹⁢(97-digit number)
72579032290239029015…20844172759579356159
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 3021502

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 3df0c2ab877ca5343b61ff570cd2660e56bf9d92e044c24586b52cbab09198ab

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 #3,021,502 on Chainz β†—
Circulating Supply:58,005,967 XPMΒ·at block #6,845,191 Β· updates every 60s
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