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Home/Chain Registry/Block #2,633,802

Block #2,633,802

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 4/28/2018, 3:00:39 PM Β· Difficulty 11.2089 Β· 4,207,044 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
9996621ae1c78eb5c1256ba21fd5bb95a7656db7c643eea0d47906023546d88a
View on Chainz β†—

Difficulty

11.208857

Transactions

1

Size

200 B

Version

2

Bits

0b3577a0

Nonce

28,335,826

Timestamp

4/28/2018, 3:00:39 PM

Confirmations

4,207,044

Merkle Root

484976d7e1365ada68914811ac1e00ecb6e404bf18947184f454e21e1adf00ea
Transactions (1)
Coinbase484976d7e1365a…54e21e1adf00ea
1 in β†’ 1 out7.9500 XPM109 B
AdfTZRPA…WPxHUjp2
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.

1.031 Γ— 10⁹⁷(98-digit number)
10312884753698420736…97913831112670000640
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
1.031 Γ— 10⁹⁷(98-digit number)
10312884753698420736…97913831112670000639
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.031 Γ— 10⁹⁷(98-digit number)
10312884753698420736…97913831112670000641
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
2.062 Γ— 10⁹⁷(98-digit number)
20625769507396841473…95827662225340001279
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.062 Γ— 10⁹⁷(98-digit number)
20625769507396841473…95827662225340001281
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
4.125 Γ— 10⁹⁷(98-digit number)
41251539014793682946…91655324450680002559
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.125 Γ— 10⁹⁷(98-digit number)
41251539014793682946…91655324450680002561
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
8.250 Γ— 10⁹⁷(98-digit number)
82503078029587365892…83310648901360005119
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
8.250 Γ— 10⁹⁷(98-digit number)
82503078029587365892…83310648901360005121
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
1.650 Γ— 10⁹⁸(99-digit number)
16500615605917473178…66621297802720010239
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.650 Γ— 10⁹⁸(99-digit number)
16500615605917473178…66621297802720010241
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
3.300 Γ— 10⁹⁸(99-digit number)
33001231211834946357…33242595605440020479
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 2633802

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 9996621ae1c78eb5c1256ba21fd5bb95a7656db7c643eea0d47906023546d88a

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 #2,633,802 on Chainz β†—
Circulating Supply:57,971,115 XPMΒ·at block #6,840,845 Β· updates every 60s
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