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Home/Chain Registry/Block #3,050,709

Block #3,050,709

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 2/13/2019, 5:47:54 AM Β· Difficulty 10.9961 Β· 3,789,678 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
aa0f6a1a3f0983fc299e3f0665dbfc111efd0346aef9367211177b7bab372e7c
View on Chainz β†—

Difficulty

10.996060

Transactions

1

Size

200 B

Version

2

Bits

0afefdd1

Nonce

172,741,489

Timestamp

2/13/2019, 5:47:54 AM

Confirmations

3,789,678

Merkle Root

023709bfbc046894b5485f90f79980eef35ed9a722d59166fb64ccd9c009b8f7
Transactions (1)
Coinbase023709bfbc0468…64ccd9c009b8f7
1 in β†’ 1 out8.2600 XPM110 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.

1.562 Γ— 10⁹⁴(95-digit number)
15624492290076674736…16910053798991331760
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
1.562 Γ— 10⁹⁴(95-digit number)
15624492290076674736…16910053798991331759
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.562 Γ— 10⁹⁴(95-digit number)
15624492290076674736…16910053798991331761
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
3.124 Γ— 10⁹⁴(95-digit number)
31248984580153349473…33820107597982663519
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.124 Γ— 10⁹⁴(95-digit number)
31248984580153349473…33820107597982663521
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
6.249 Γ— 10⁹⁴(95-digit number)
62497969160306698947…67640215195965327039
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.249 Γ— 10⁹⁴(95-digit number)
62497969160306698947…67640215195965327041
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
1.249 Γ— 10⁹⁡(96-digit number)
12499593832061339789…35280430391930654079
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.249 Γ— 10⁹⁡(96-digit number)
12499593832061339789…35280430391930654081
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
2.499 Γ— 10⁹⁡(96-digit number)
24999187664122679578…70560860783861308159
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.499 Γ— 10⁹⁡(96-digit number)
24999187664122679578…70560860783861308161
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
4.999 Γ— 10⁹⁡(96-digit number)
49998375328245359157…41121721567722616319
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 3050709

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 aa0f6a1a3f0983fc299e3f0665dbfc111efd0346aef9367211177b7bab372e7c

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 #3,050,709 on Chainz β†—
Circulating Supply:57,967,418 XPMΒ·at block #6,840,386 Β· updates every 60s
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