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Home/Chain Registry/Block #2,134,333

Block #2,134,333

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/27/2017, 4:09:29 AM Β· Difficulty 10.9089 Β· 4,708,570 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
e48c276ed9e2abfe8977a0acbd8bed4bdfebbd6c7e2c68b22243c5afde57fb25
View on Chainz β†—

Difficulty

10.908936

Transactions

2

Size

724 B

Version

2

Bits

0ae8b002

Nonce

1,369,352,759

Timestamp

5/27/2017, 4:09:29 AM

Confirmations

4,708,570

Merkle Root

ef11294c95161dcc8f897794401060b9a131d0d8377ce2ecfaff4ab2a388a766
Transactions (2)
Coinbase7b3789015757bc…a4e2ec884f13fe
1 in β†’ 1 out8.4000 XPM109 B
ATqQKb6R…4GCm5uAJ
5ddf7052934bff…bfda4b7f6e85f4
3 in β†’ 2 out416.3278 XPM523 B
ATEUwwo1…BiseCEDqAZAUi21T…4Mwjwt9m
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.

3.140 Γ— 10⁹⁸(99-digit number)
31402915431225424340…20827666055197163520
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
3.140 Γ— 10⁹⁸(99-digit number)
31402915431225424340…20827666055197163519
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.140 Γ— 10⁹⁸(99-digit number)
31402915431225424340…20827666055197163521
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
6.280 Γ— 10⁹⁸(99-digit number)
62805830862450848681…41655332110394327039
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.280 Γ— 10⁹⁸(99-digit number)
62805830862450848681…41655332110394327041
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
1.256 Γ— 10⁹⁹(100-digit number)
12561166172490169736…83310664220788654079
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.256 Γ— 10⁹⁹(100-digit number)
12561166172490169736…83310664220788654081
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
2.512 Γ— 10⁹⁹(100-digit number)
25122332344980339472…66621328441577308159
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.512 Γ— 10⁹⁹(100-digit number)
25122332344980339472…66621328441577308161
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
5.024 Γ— 10⁹⁹(100-digit number)
50244664689960678944…33242656883154616319
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.024 Γ— 10⁹⁹(100-digit number)
50244664689960678944…33242656883154616321
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
1.004 Γ— 10¹⁰⁰(101-digit number)
10048932937992135788…66485313766309232639
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 2134333

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 e48c276ed9e2abfe8977a0acbd8bed4bdfebbd6c7e2c68b22243c5afde57fb25

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 #2,134,333 on Chainz β†—
Circulating Supply:57,987,571 XPMΒ·at block #6,842,902 Β· updates every 60s
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