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Home/Chain Registry/Block #2,837,761

Block #2,837,761

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 9/13/2018, 6:02:47 PM Β· Difficulty 11.7160 Β· 3,993,508 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
5a1aa611cd7129de705419b4386e21292705f99b961ac3f8adb349679923eefa
View on Chainz β†—

Difficulty

11.715975

Transactions

2

Size

539 B

Version

2

Bits

0bb74a2a

Nonce

269,369,691

Timestamp

9/13/2018, 6:02:47 PM

Confirmations

3,993,508

Merkle Root

ece4a8c0460f72067cd5b4c3a9e5fe18a143808f91c87f3c9d413591e19263d2
Transactions (2)
Coinbaseb68b29298407dd…c6acd58c8d93c4
1 in β†’ 1 out7.2800 XPM110 B
AZtxQr2F…7grUWrUz
7ee70b8dece691…2c8c242cf174e9
2 in β†’ 2 out11.8000 XPM339 B
AM6XD26m…RcphfPC1AGNLUNHn…fCxE1YRt
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.

8.236 Γ— 10⁹³(94-digit number)
82364184718699251486…57611138955615717360
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
8.236 Γ— 10⁹³(94-digit number)
82364184718699251486…57611138955615717359
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
8.236 Γ— 10⁹³(94-digit number)
82364184718699251486…57611138955615717361
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
1.647 Γ— 10⁹⁴(95-digit number)
16472836943739850297…15222277911231434719
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.647 Γ— 10⁹⁴(95-digit number)
16472836943739850297…15222277911231434721
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
3.294 Γ— 10⁹⁴(95-digit number)
32945673887479700594…30444555822462869439
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.294 Γ— 10⁹⁴(95-digit number)
32945673887479700594…30444555822462869441
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
6.589 Γ— 10⁹⁴(95-digit number)
65891347774959401189…60889111644925738879
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.589 Γ— 10⁹⁴(95-digit number)
65891347774959401189…60889111644925738881
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
1.317 Γ— 10⁹⁡(96-digit number)
13178269554991880237…21778223289851477759
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.317 Γ— 10⁹⁡(96-digit number)
13178269554991880237…21778223289851477761
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
2.635 Γ— 10⁹⁡(96-digit number)
26356539109983760475…43556446579702955519
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 2837761

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 5a1aa611cd7129de705419b4386e21292705f99b961ac3f8adb349679923eefa

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 #2,837,761 on Chainz β†—
Circulating Supply:57,894,297 XPMΒ·at block #6,831,268 Β· updates every 60s
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