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Home/Chain Registry/Block #1,852,625

Block #1,852,625

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 11/17/2016, 5:35:18 AM Β· Difficulty 10.6315 Β· 4,974,551 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
55e2135c373fd87f27f47325f9b85d11345cb19e7c0d5eba2e6df29334764ee9
View on Chainz β†—

Difficulty

10.631492

Transactions

1

Size

202 B

Version

2

Bits

0aa1a974

Nonce

180,010,391

Timestamp

11/17/2016, 5:35:18 AM

Confirmations

4,974,551

Merkle Root

fc66d5abcc9d4a797b6dd161702fac734fe7b52b6ea2c780ca5ec324b89dad0c
Transactions (1)
Coinbasefc66d5abcc9d4a…5ec324b89dad0c
1 in β†’ 1 out8.8300 XPM110 B
AKjDrjcE…runS3jNV
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.

4.529 Γ— 10⁹⁸(99-digit number)
45292039883343091740…76799001658753024000
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
4.529 Γ— 10⁹⁸(99-digit number)
45292039883343091740…76799001658753023999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.529 Γ— 10⁹⁸(99-digit number)
45292039883343091740…76799001658753024001
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
9.058 Γ— 10⁹⁸(99-digit number)
90584079766686183481…53598003317506047999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
9.058 Γ— 10⁹⁸(99-digit number)
90584079766686183481…53598003317506048001
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
1.811 Γ— 10⁹⁹(100-digit number)
18116815953337236696…07196006635012095999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.811 Γ— 10⁹⁹(100-digit number)
18116815953337236696…07196006635012096001
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
3.623 Γ— 10⁹⁹(100-digit number)
36233631906674473392…14392013270024191999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.623 Γ— 10⁹⁹(100-digit number)
36233631906674473392…14392013270024192001
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
7.246 Γ— 10⁹⁹(100-digit number)
72467263813348946785…28784026540048383999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
7.246 Γ— 10⁹⁹(100-digit number)
72467263813348946785…28784026540048384001
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10
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 1852625

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 55e2135c373fd87f27f47325f9b85d11345cb19e7c0d5eba2e6df29334764ee9

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 #1,852,625 on Chainz β†—
Circulating Supply:57,861,505 XPMΒ·at block #6,827,175 Β· updates every 60s
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