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Home/Chain Registry/Block #2,843,256

Block #2,843,256

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 9/17/2018, 10:38:22 AM Β· Difficulty 11.7262 Β· 3,993,414 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
701ca2c53b4134f56a73da3522d85d6f9d2b5c8d5311e102f530d69d4a790b49
View on Chainz β†—

Difficulty

11.726185

Transactions

1

Size

201 B

Version

2

Bits

0bb9e749

Nonce

2,142,489,666

Timestamp

9/17/2018, 10:38:22 AM

Confirmations

3,993,414

Merkle Root

0e57b6b71593de1ccf8415dcbab7d75d42e598c5a17bfbb62c07810fcea513e2
Transactions (1)
Coinbase0e57b6b71593de…07810fcea513e2
1 in β†’ 1 out7.2600 XPM110 B
AUmJmxKY…bigt5nrg
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.

1.209 Γ— 10⁹⁷(98-digit number)
12096817488754097355…50580132050990182400
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
1.209 Γ— 10⁹⁷(98-digit number)
12096817488754097355…50580132050990182399
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.209 Γ— 10⁹⁷(98-digit number)
12096817488754097355…50580132050990182401
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
2.419 Γ— 10⁹⁷(98-digit number)
24193634977508194710…01160264101980364799
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.419 Γ— 10⁹⁷(98-digit number)
24193634977508194710…01160264101980364801
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
4.838 Γ— 10⁹⁷(98-digit number)
48387269955016389421…02320528203960729599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.838 Γ— 10⁹⁷(98-digit number)
48387269955016389421…02320528203960729601
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
9.677 Γ— 10⁹⁷(98-digit number)
96774539910032778842…04641056407921459199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
9.677 Γ— 10⁹⁷(98-digit number)
96774539910032778842…04641056407921459201
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
1.935 Γ— 10⁹⁸(99-digit number)
19354907982006555768…09282112815842918399
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.935 Γ— 10⁹⁸(99-digit number)
19354907982006555768…09282112815842918401
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
3.870 Γ— 10⁹⁸(99-digit number)
38709815964013111537…18564225631685836799
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 2843256

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 701ca2c53b4134f56a73da3522d85d6f9d2b5c8d5311e102f530d69d4a790b49

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 #2,843,256 on Chainz β†—
Circulating Supply:57,937,638 XPMΒ·at block #6,836,669 Β· updates every 60s
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