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Home/Chain Registry/Block #2,717,017

Block #2,717,017

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 6/22/2018, 10:10:44 PM Β· Difficulty 11.6149 Β· 4,128,630 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
e0444507f05c799eb65f123e3499d44755e84dddb82d4189411369f9fc6f17bd
View on Chainz β†—

Difficulty

11.614891

Transactions

1

Size

200 B

Version

2

Bits

0b9d697f

Nonce

117,398,092

Timestamp

6/22/2018, 10:10:44 PM

Confirmations

4,128,630

Merkle Root

0505830bcafa85191e2d2332f389af77b650d8422d853aad8947529f6edd1aca
Transactions (1)
Coinbase0505830bcafa85…47529f6edd1aca
1 in β†’ 1 out7.4000 XPM110 B
AWoWq45N…7drYEqfr
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.

3.616 Γ— 10⁹⁴(95-digit number)
36166361230252162202…15002921006289248880
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
3.616 Γ— 10⁹⁴(95-digit number)
36166361230252162202…15002921006289248879
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.616 Γ— 10⁹⁴(95-digit number)
36166361230252162202…15002921006289248881
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
7.233 Γ— 10⁹⁴(95-digit number)
72332722460504324405…30005842012578497759
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
7.233 Γ— 10⁹⁴(95-digit number)
72332722460504324405…30005842012578497761
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
1.446 Γ— 10⁹⁡(96-digit number)
14466544492100864881…60011684025156995519
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.446 Γ— 10⁹⁡(96-digit number)
14466544492100864881…60011684025156995521
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
2.893 Γ— 10⁹⁡(96-digit number)
28933088984201729762…20023368050313991039
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.893 Γ— 10⁹⁡(96-digit number)
28933088984201729762…20023368050313991041
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
5.786 Γ— 10⁹⁡(96-digit number)
57866177968403459524…40046736100627982079
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.786 Γ— 10⁹⁡(96-digit number)
57866177968403459524…40046736100627982081
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
1.157 Γ— 10⁹⁢(97-digit number)
11573235593680691904…80093472201255964159
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 2717017

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 e0444507f05c799eb65f123e3499d44755e84dddb82d4189411369f9fc6f17bd

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 #2,717,017 on Chainz β†—
Circulating Supply:58,009,625 XPMΒ·at block #6,845,646 Β· updates every 60s
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