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Home/Chain Registry/Block #3,048,657

Block #3,048,657

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 2/11/2019, 5:32:21 PM Β· Difficulty 10.9961 Β· 3,794,544 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
333b0260bf65a1f71f0fd6c0e07ff2bb94bfb792f693f61c3509f7400d10e66f
View on Chainz β†—

Difficulty

10.996093

Transactions

1

Size

199 B

Version

2

Bits

0afefff2

Nonce

606,362,291

Timestamp

2/11/2019, 5:32:21 PM

Confirmations

3,794,544

Merkle Root

3049d439bc055a2a553da146c6482af33f7d85907d7eb3cf72a201a6de8f4d54
Transactions (1)
Coinbase3049d439bc055a…a201a6de8f4d54
1 in β†’ 1 out8.2600 XPM109 B
AUMQRepm…tAfKmdW1
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.

3.703 Γ— 10⁹⁡(96-digit number)
37037241897413991938…55773327976154440320
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
3.703 Γ— 10⁹⁡(96-digit number)
37037241897413991938…55773327976154440319
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.703 Γ— 10⁹⁡(96-digit number)
37037241897413991938…55773327976154440321
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
7.407 Γ— 10⁹⁡(96-digit number)
74074483794827983877…11546655952308880639
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
7.407 Γ— 10⁹⁡(96-digit number)
74074483794827983877…11546655952308880641
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
1.481 Γ— 10⁹⁢(97-digit number)
14814896758965596775…23093311904617761279
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.481 Γ— 10⁹⁢(97-digit number)
14814896758965596775…23093311904617761281
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
2.962 Γ— 10⁹⁢(97-digit number)
29629793517931193551…46186623809235522559
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.962 Γ— 10⁹⁢(97-digit number)
29629793517931193551…46186623809235522561
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
5.925 Γ— 10⁹⁢(97-digit number)
59259587035862387102…92373247618471045119
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.925 Γ— 10⁹⁢(97-digit number)
59259587035862387102…92373247618471045121
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
1.185 Γ— 10⁹⁷(98-digit number)
11851917407172477420…84746495236942090239
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 3048657

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 333b0260bf65a1f71f0fd6c0e07ff2bb94bfb792f693f61c3509f7400d10e66f

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 #3,048,657 on Chainz β†—
Circulating Supply:57,989,979 XPMΒ·at block #6,843,200 Β· updates every 60s
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