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Home/Chain Registry/Block #2,133,576

Block #2,133,576

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 5/26/2017, 3:02:51 PM Β· Difficulty 10.9094 Β· 4,707,584 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
aee2fd342f03b0036c2e47634890c558ea8b81302f3670b4fdffcc259cd5da7f
View on Chainz β†—

Difficulty

10.909445

Transactions

1

Size

199 B

Version

2

Bits

0ae8d165

Nonce

374,313,558

Timestamp

5/26/2017, 3:02:51 PM

Confirmations

4,707,584

Merkle Root

6e2204905c63db932bec1f87cd26549841f4cf2f57ae1d1bd4d099ab533c71ca
Transactions (1)
Coinbase6e2204905c63db…d099ab533c71ca
1 in β†’ 1 out8.3900 XPM109 B
APg4xTj3…fm6LwaSx
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.

4.220 Γ— 10⁹⁴(95-digit number)
42205182769129924238…34833654768042532580
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
4.220 Γ— 10⁹⁴(95-digit number)
42205182769129924238…34833654768042532579
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.220 Γ— 10⁹⁴(95-digit number)
42205182769129924238…34833654768042532581
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
8.441 Γ— 10⁹⁴(95-digit number)
84410365538259848477…69667309536085065159
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
8.441 Γ— 10⁹⁴(95-digit number)
84410365538259848477…69667309536085065161
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
1.688 Γ— 10⁹⁡(96-digit number)
16882073107651969695…39334619072170130319
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.688 Γ— 10⁹⁡(96-digit number)
16882073107651969695…39334619072170130321
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
3.376 Γ— 10⁹⁡(96-digit number)
33764146215303939390…78669238144340260639
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.376 Γ— 10⁹⁡(96-digit number)
33764146215303939390…78669238144340260641
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
6.752 Γ— 10⁹⁡(96-digit number)
67528292430607878781…57338476288680521279
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
6.752 Γ— 10⁹⁡(96-digit number)
67528292430607878781…57338476288680521281
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 2133576

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 aee2fd342f03b0036c2e47634890c558ea8b81302f3670b4fdffcc259cd5da7f

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 #2,133,576 on Chainz β†—
Circulating Supply:57,973,644 XPMΒ·at block #6,841,159 Β· updates every 60s
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