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Home/Chain Registry/Block #2,833,096

Block #2,833,096

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 9/10/2018, 12:38:22 PM Β· Difficulty 11.7146 Β· 4,012,554 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
a751726b29ff620944bba0d0dd0e5f35f4d806fd619885318e33a5390e5389d5
View on Chainz β†—

Difficulty

11.714638

Transactions

1

Size

200 B

Version

2

Bits

0bb6f284

Nonce

495,411,744

Timestamp

9/10/2018, 12:38:22 PM

Confirmations

4,012,554

Merkle Root

98475feb81255a34b11aee59a9536da6e574b468ba3c1fe182f7ebdc87531da1
Transactions (1)
Coinbase98475feb81255a…f7ebdc87531da1
1 in β†’ 1 out7.2700 XPM110 B
AZueUXg5…oJGTTjgN
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.

1.967 Γ— 10⁹⁡(96-digit number)
19675532461579460512…66697902286661920000
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
1.967 Γ— 10⁹⁡(96-digit number)
19675532461579460512…66697902286661919999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.967 Γ— 10⁹⁡(96-digit number)
19675532461579460512…66697902286661920001
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
3.935 Γ— 10⁹⁡(96-digit number)
39351064923158921025…33395804573323839999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.935 Γ— 10⁹⁡(96-digit number)
39351064923158921025…33395804573323840001
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
7.870 Γ— 10⁹⁡(96-digit number)
78702129846317842050…66791609146647679999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
7.870 Γ— 10⁹⁡(96-digit number)
78702129846317842050…66791609146647680001
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
1.574 Γ— 10⁹⁢(97-digit number)
15740425969263568410…33583218293295359999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.574 Γ— 10⁹⁢(97-digit number)
15740425969263568410…33583218293295360001
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
3.148 Γ— 10⁹⁢(97-digit number)
31480851938527136820…67166436586590719999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.148 Γ— 10⁹⁢(97-digit number)
31480851938527136820…67166436586590720001
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
6.296 Γ— 10⁹⁢(97-digit number)
62961703877054273640…34332873173181439999
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 2833096

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 a751726b29ff620944bba0d0dd0e5f35f4d806fd619885318e33a5390e5389d5

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 #2,833,096 on Chainz β†—
Circulating Supply:58,009,649 XPMΒ·at block #6,845,649 Β· updates every 60s
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