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Home/Chain Registry/Block #2,943,888

Block #2,943,888

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 11/29/2018, 3:12:42 AM Β· Difficulty 11.3947 Β· 3,881,738 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
47dd6ccee30f7a7bf2fb338fcf417b99f8cb932fc30418b3326f9e519014f496
View on Chainz β†—

Difficulty

11.394703

Transactions

1

Size

202 B

Version

2

Bits

0b650b41

Nonce

1,231,598,606

Timestamp

11/29/2018, 3:12:42 AM

Confirmations

3,881,738

Merkle Root

13b4e489b518a560d2972fbfcd79ac859ffceb88e1ecf1655ebab191b449b951
Transactions (1)
Coinbase13b4e489b518a5…bab191b449b951
1 in β†’ 1 out7.6900 XPM110 B
AbXwmGxD…4XXYP765
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.

2.395 Γ— 10⁹⁸(99-digit number)
23959029178435963851…05220301796123607040
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
2.395 Γ— 10⁹⁸(99-digit number)
23959029178435963851…05220301796123607039
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.395 Γ— 10⁹⁸(99-digit number)
23959029178435963851…05220301796123607041
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
4.791 Γ— 10⁹⁸(99-digit number)
47918058356871927702…10440603592247214079
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.791 Γ— 10⁹⁸(99-digit number)
47918058356871927702…10440603592247214081
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
9.583 Γ— 10⁹⁸(99-digit number)
95836116713743855405…20881207184494428159
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
9.583 Γ— 10⁹⁸(99-digit number)
95836116713743855405…20881207184494428161
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
1.916 Γ— 10⁹⁹(100-digit number)
19167223342748771081…41762414368988856319
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.916 Γ— 10⁹⁹(100-digit number)
19167223342748771081…41762414368988856321
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
3.833 Γ— 10⁹⁹(100-digit number)
38334446685497542162…83524828737977712639
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.833 Γ— 10⁹⁹(100-digit number)
38334446685497542162…83524828737977712641
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
7.666 Γ— 10⁹⁹(100-digit number)
76668893370995084324…67049657475955425279
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 2943888

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 47dd6ccee30f7a7bf2fb338fcf417b99f8cb932fc30418b3326f9e519014f496

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 #2,943,888 on Chainz β†—
Circulating Supply:57,849,111 XPMΒ·at block #6,825,625 Β· updates every 60s
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