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Home/Chain Registry/Block #2,785,622

Block #2,785,622

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 8/9/2018, 12:41:39 AM Β· Difficulty 11.6719 Β· 4,052,870 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
16bc64128ddbb8f8a64e0a9b200b9583ed4e0934d830588fe802cdde8092c390
View on Chainz β†—

Difficulty

11.671934

Transactions

1

Size

200 B

Version

2

Bits

0bac03d9

Nonce

899,067,421

Timestamp

8/9/2018, 12:41:39 AM

Confirmations

4,052,870

Merkle Root

1acd589e806813c118d9053895628441d0ac8ae36a21f9ff0a86df10871eb703
Transactions (1)
Coinbase1acd589e806813…86df10871eb703
1 in β†’ 1 out7.3300 XPM110 B
AV8pW6xs…CmuVVGGq
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.

5.582 Γ— 10⁹³(94-digit number)
55823759938607052384…29622909772843886080
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
5.582 Γ— 10⁹³(94-digit number)
55823759938607052384…29622909772843886079
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.582 Γ— 10⁹³(94-digit number)
55823759938607052384…29622909772843886081
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
1.116 Γ— 10⁹⁴(95-digit number)
11164751987721410476…59245819545687772159
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.116 Γ— 10⁹⁴(95-digit number)
11164751987721410476…59245819545687772161
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
2.232 Γ— 10⁹⁴(95-digit number)
22329503975442820953…18491639091375544319
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.232 Γ— 10⁹⁴(95-digit number)
22329503975442820953…18491639091375544321
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
4.465 Γ— 10⁹⁴(95-digit number)
44659007950885641907…36983278182751088639
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.465 Γ— 10⁹⁴(95-digit number)
44659007950885641907…36983278182751088641
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
8.931 Γ— 10⁹⁴(95-digit number)
89318015901771283815…73966556365502177279
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
8.931 Γ— 10⁹⁴(95-digit number)
89318015901771283815…73966556365502177281
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
1.786 Γ— 10⁹⁡(96-digit number)
17863603180354256763…47933112731004354559
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 2785622

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 16bc64128ddbb8f8a64e0a9b200b9583ed4e0934d830588fe802cdde8092c390

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 #2,785,622 on Chainz β†—
Circulating Supply:57,952,208 XPMΒ·at block #6,838,491 Β· updates every 60s
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