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Home/Chain Registry/Block #2,272,834

Block #2,272,834

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 8/29/2017, 4:19:22 AM Β· Difficulty 10.9543 Β· 4,565,815 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
f1888d3d9aca5c0246dd3eddb1355b83cb7ca2c37c951289c17eba8b6d4b0e27
View on Chainz β†—

Difficulty

10.954323

Transactions

1

Size

200 B

Version

2

Bits

0af44e84

Nonce

1,644,664,277

Timestamp

8/29/2017, 4:19:22 AM

Confirmations

4,565,815

Merkle Root

42310a4e53e92a169fff13787940e10858bb57ce03f0afba52877a92015d78fb
Transactions (1)
Coinbase42310a4e53e92a…877a92015d78fb
1 in β†’ 1 out8.3200 XPM109 B
ARwiGpz8…JWiNDvEV
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.

8.412 Γ— 10⁹⁡(96-digit number)
84128757986449782021…34086918433049396480
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
8.412 Γ— 10⁹⁡(96-digit number)
84128757986449782021…34086918433049396479
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
8.412 Γ— 10⁹⁡(96-digit number)
84128757986449782021…34086918433049396481
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
1.682 Γ— 10⁹⁢(97-digit number)
16825751597289956404…68173836866098792959
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.682 Γ— 10⁹⁢(97-digit number)
16825751597289956404…68173836866098792961
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
3.365 Γ— 10⁹⁢(97-digit number)
33651503194579912808…36347673732197585919
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.365 Γ— 10⁹⁢(97-digit number)
33651503194579912808…36347673732197585921
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
6.730 Γ— 10⁹⁢(97-digit number)
67303006389159825617…72695347464395171839
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.730 Γ— 10⁹⁢(97-digit number)
67303006389159825617…72695347464395171841
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
1.346 Γ— 10⁹⁷(98-digit number)
13460601277831965123…45390694928790343679
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.346 Γ— 10⁹⁷(98-digit number)
13460601277831965123…45390694928790343681
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
2.692 Γ— 10⁹⁷(98-digit number)
26921202555663930246…90781389857580687359
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 2272834

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 f1888d3d9aca5c0246dd3eddb1355b83cb7ca2c37c951289c17eba8b6d4b0e27

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 #2,272,834 on Chainz β†—
Circulating Supply:57,953,450 XPMΒ·at block #6,838,648 Β· updates every 60s
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