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Home/Chain Registry/Block #2,818,065

Block #2,818,065

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 8/31/2018, 7:02:29 AM Β· Difficulty 11.6969 Β· 4,023,877 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
159fab5aa5edcbcc3a2601fd4a34958d6b08ea36245fdb27438297784e681c6d
View on Chainz β†—

Difficulty

11.696890

Transactions

1

Size

200 B

Version

2

Bits

0bb2675b

Nonce

809,001,950

Timestamp

8/31/2018, 7:02:29 AM

Confirmations

4,023,877

Merkle Root

489fede838b72c07e99f391420a429cd00abd88120c7e6c55916ea9af1af7a80
Transactions (1)
Coinbase489fede838b72c…16ea9af1af7a80
1 in β†’ 1 out7.3000 XPM110 B
AZzmygFE…YvcpDdo1
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.

2.561 Γ— 10⁹⁴(95-digit number)
25613836482129771222…95466402551789040000
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
2.561 Γ— 10⁹⁴(95-digit number)
25613836482129771222…95466402551789039999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.561 Γ— 10⁹⁴(95-digit number)
25613836482129771222…95466402551789040001
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
5.122 Γ— 10⁹⁴(95-digit number)
51227672964259542445…90932805103578079999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.122 Γ— 10⁹⁴(95-digit number)
51227672964259542445…90932805103578080001
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
1.024 Γ— 10⁹⁡(96-digit number)
10245534592851908489…81865610207156159999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.024 Γ— 10⁹⁡(96-digit number)
10245534592851908489…81865610207156160001
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
2.049 Γ— 10⁹⁡(96-digit number)
20491069185703816978…63731220414312319999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.049 Γ— 10⁹⁡(96-digit number)
20491069185703816978…63731220414312320001
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
4.098 Γ— 10⁹⁡(96-digit number)
40982138371407633956…27462440828624639999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.098 Γ— 10⁹⁡(96-digit number)
40982138371407633956…27462440828624640001
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
8.196 Γ— 10⁹⁡(96-digit number)
81964276742815267912…54924881657249279999
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 2818065

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 159fab5aa5edcbcc3a2601fd4a34958d6b08ea36245fdb27438297784e681c6d

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 #2,818,065 on Chainz β†—
Circulating Supply:57,979,916 XPMΒ·at block #6,841,941 Β· updates every 60s
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