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Home/Chain Registry/Block #2,801,988

Block #2,801,988

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 8/20/2018, 9:47:14 AM Β· Difficulty 11.6712 Β· 4,040,180 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
c2b133aaa94fd6d5af76599fdc0b8d12bd0cfd73da39ff7b26a21afc678347e7
View on Chainz β†—

Difficulty

11.671208

Transactions

1

Size

200 B

Version

2

Bits

0babd446

Nonce

410,176,363

Timestamp

8/20/2018, 9:47:14 AM

Confirmations

4,040,180

Merkle Root

afd8f4d39669838573829223888bd681ebb7ed3893f492b6a178cae795793b4c
Transactions (1)
Coinbaseafd8f4d3966983…78cae795793b4c
1 in β†’ 1 out7.3300 XPM109 B
AJjQMgn8…iD8dg8vD
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.

4.439 Γ— 10⁹⁷(98-digit number)
44399684115382515393…45464718296826839040
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
4.439 Γ— 10⁹⁷(98-digit number)
44399684115382515393…45464718296826839039
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.439 Γ— 10⁹⁷(98-digit number)
44399684115382515393…45464718296826839041
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
8.879 Γ— 10⁹⁷(98-digit number)
88799368230765030787…90929436593653678079
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
8.879 Γ— 10⁹⁷(98-digit number)
88799368230765030787…90929436593653678081
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
1.775 Γ— 10⁹⁸(99-digit number)
17759873646153006157…81858873187307356159
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.775 Γ— 10⁹⁸(99-digit number)
17759873646153006157…81858873187307356161
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
3.551 Γ— 10⁹⁸(99-digit number)
35519747292306012314…63717746374614712319
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.551 Γ— 10⁹⁸(99-digit number)
35519747292306012314…63717746374614712321
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
7.103 Γ— 10⁹⁸(99-digit number)
71039494584612024629…27435492749229424639
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
7.103 Γ— 10⁹⁸(99-digit number)
71039494584612024629…27435492749229424641
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
1.420 Γ— 10⁹⁹(100-digit number)
14207898916922404925…54870985498458849279
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 2801988

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 c2b133aaa94fd6d5af76599fdc0b8d12bd0cfd73da39ff7b26a21afc678347e7

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 #2,801,988 on Chainz β†—
Circulating Supply:57,981,735 XPMΒ·at block #6,842,167 Β· updates every 60s
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