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Home/Chain Registry/Block #2,152,284

Block #2,152,284

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 6/8/2017, 10:34:56 PM Β· Difficulty 10.9012 Β· 4,681,182 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
fa8cefda968fc2642ec104cdccd31c59a0c4ee68e72b662d186202b4563e69ab
View on Chainz β†—

Difficulty

10.901248

Transactions

2

Size

424 B

Version

2

Bits

0ae6b833

Nonce

1,053,412,704

Timestamp

6/8/2017, 10:34:56 PM

Confirmations

4,681,182

Merkle Root

1e1e36e0598c39192d5afe4120776c319a2fe396284c3cbdb4afbdc8ca65ae81
Transactions (2)
Coinbasef7c46e89106938…94e8b6c0c0f027
1 in β†’ 1 out8.4100 XPM109 B
AKHeFQ8J…xe73MnEN
95b247753a7126…5928a43d5090f3
1 in β†’ 2 out20883.5764 XPM225 B
AUwoKL2D…GhfKD7SnAWEQDNJ4…cinXi5vt
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.

6.123 Γ— 10⁹⁴(95-digit number)
61237105326707132863…44246973176944746880
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
6.123 Γ— 10⁹⁴(95-digit number)
61237105326707132863…44246973176944746879
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
6.123 Γ— 10⁹⁴(95-digit number)
61237105326707132863…44246973176944746881
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
1.224 Γ— 10⁹⁡(96-digit number)
12247421065341426572…88493946353889493759
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.224 Γ— 10⁹⁡(96-digit number)
12247421065341426572…88493946353889493761
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
2.449 Γ— 10⁹⁡(96-digit number)
24494842130682853145…76987892707778987519
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.449 Γ— 10⁹⁡(96-digit number)
24494842130682853145…76987892707778987521
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
4.898 Γ— 10⁹⁡(96-digit number)
48989684261365706290…53975785415557975039
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.898 Γ— 10⁹⁡(96-digit number)
48989684261365706290…53975785415557975041
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
9.797 Γ— 10⁹⁡(96-digit number)
97979368522731412581…07951570831115950079
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
9.797 Γ— 10⁹⁡(96-digit number)
97979368522731412581…07951570831115950081
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 2152284

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 fa8cefda968fc2642ec104cdccd31c59a0c4ee68e72b662d186202b4563e69ab

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 #2,152,284 on Chainz β†—
Circulating Supply:57,911,929 XPMΒ·at block #6,833,465 Β· updates every 60s
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