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Home/Chain Registry/Block #2,834,088

Block #2,834,088

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 9/11/2018, 4:55:15 AM Β· Difficulty 11.7155 Β· 4,007,309 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
ffd3ae76bd2fd963f483a87fda67ccc4e4ce51ad5796f2f713eec139dd757a3f
View on Chainz β†—

Difficulty

11.715548

Transactions

1

Size

200 B

Version

2

Bits

0bb72e27

Nonce

1,539,547,074

Timestamp

9/11/2018, 4:55:15 AM

Confirmations

4,007,309

Merkle Root

a53d30628e3f6c00a032c06836c2ac28c12f82400717300714b23835309f8d7b
Transactions (1)
Coinbasea53d30628e3f6c…b23835309f8d7b
1 in β†’ 1 out7.2700 XPM109 B
AQJzn7hV…diTsNAHC
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.

6.052 Γ— 10⁹⁢(97-digit number)
60529444716445957444…12917784219845304320
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
6.052 Γ— 10⁹⁢(97-digit number)
60529444716445957444…12917784219845304319
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
6.052 Γ— 10⁹⁢(97-digit number)
60529444716445957444…12917784219845304321
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
1.210 Γ— 10⁹⁷(98-digit number)
12105888943289191488…25835568439690608639
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.210 Γ— 10⁹⁷(98-digit number)
12105888943289191488…25835568439690608641
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
2.421 Γ— 10⁹⁷(98-digit number)
24211777886578382977…51671136879381217279
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.421 Γ— 10⁹⁷(98-digit number)
24211777886578382977…51671136879381217281
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
4.842 Γ— 10⁹⁷(98-digit number)
48423555773156765955…03342273758762434559
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.842 Γ— 10⁹⁷(98-digit number)
48423555773156765955…03342273758762434561
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
9.684 Γ— 10⁹⁷(98-digit number)
96847111546313531911…06684547517524869119
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
9.684 Γ— 10⁹⁷(98-digit number)
96847111546313531911…06684547517524869121
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
1.936 Γ— 10⁹⁸(99-digit number)
19369422309262706382…13369095035049738239
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 2834088

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 ffd3ae76bd2fd963f483a87fda67ccc4e4ce51ad5796f2f713eec139dd757a3f

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 #2,834,088 on Chainz β†—
Circulating Supply:57,975,548 XPMΒ·at block #6,841,396 Β· updates every 60s
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