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Home/Chain Registry/Block #2,717,214

Block #2,717,214

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 6/23/2018, 1:26:25 AM Β· Difficulty 11.6150 Β· 4,116,349 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
5baa54a9245e4940e9c0953884cd86d8c18d93fa8a6d261fd8d6c1dd58d0ad3e
View on Chainz β†—

Difficulty

11.614986

Transactions

2

Size

868 B

Version

2

Bits

0b9d6fb5

Nonce

1,119,552,558

Timestamp

6/23/2018, 1:26:25 AM

Confirmations

4,116,349

Merkle Root

af9261ad9765a62e4732306cb804876e8030d6f1f5516cb6f546f2bc1c4e8edf
Transactions (2)
Coinbase7073e24d2a407c…e56bcc329ba620
1 in β†’ 1 out7.4100 XPM110 B
AKMJHJrs…eH5Ui2YV
3e04b329521089…b2203fdc9e3f75
4 in β†’ 2 out1075.6266 XPM667 B
AbiZw7N1…HPacQJfkAPaiW6MM…ewpLq3fH
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.

7.289 Γ— 10⁹⁡(96-digit number)
72898222289490707770…79928983248961679360
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
7.289 Γ— 10⁹⁡(96-digit number)
72898222289490707770…79928983248961679359
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
7.289 Γ— 10⁹⁡(96-digit number)
72898222289490707770…79928983248961679361
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
1.457 Γ— 10⁹⁢(97-digit number)
14579644457898141554…59857966497923358719
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.457 Γ— 10⁹⁢(97-digit number)
14579644457898141554…59857966497923358721
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
2.915 Γ— 10⁹⁢(97-digit number)
29159288915796283108…19715932995846717439
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.915 Γ— 10⁹⁢(97-digit number)
29159288915796283108…19715932995846717441
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
5.831 Γ— 10⁹⁢(97-digit number)
58318577831592566216…39431865991693434879
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.831 Γ— 10⁹⁢(97-digit number)
58318577831592566216…39431865991693434881
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
1.166 Γ— 10⁹⁷(98-digit number)
11663715566318513243…78863731983386869759
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.166 Γ— 10⁹⁷(98-digit number)
11663715566318513243…78863731983386869761
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
2.332 Γ— 10⁹⁷(98-digit number)
23327431132637026486…57727463966773739519
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 2717214

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 5baa54a9245e4940e9c0953884cd86d8c18d93fa8a6d261fd8d6c1dd58d0ad3e

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 #2,717,214 on Chainz β†—
Circulating Supply:57,912,705 XPMΒ·at block #6,833,562 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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