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Home/Chain Registry/Block #2,272,049

Block #2,272,049

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 8/28/2017, 3:39:37 PM Β· Difficulty 10.9541 Β· 4,558,448 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
13ddab93e4afb2d42d060b37e80558d03e4a05aaaaf0c4e09606c899254ff7ed
View on Chainz β†—

Difficulty

10.954069

Transactions

2

Size

424 B

Version

2

Bits

0af43de6

Nonce

2,051,706,056

Timestamp

8/28/2017, 3:39:37 PM

Confirmations

4,558,448

Merkle Root

a32d5faa18b5dba04ade8821e685fdab60f3af4888f4a6003cdec72b6842448f
Transactions (2)
Coinbase4731102ea6dafa…e6b25e2b94a65e
1 in β†’ 1 out8.3300 XPM109 B
AJpnwRZF…u6PgGDHw
ce676720015462…6164bc2a11e6b1
1 in β†’ 2 out2.8323 XPM225 B
AV5bDXsF…JGKHA1dBAGfYzJRh…4uodP7T3
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.

6.906 Γ— 10⁹³(94-digit number)
69068515050913338993…38838588698120003250
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
6.906 Γ— 10⁹³(94-digit number)
69068515050913338993…38838588698120003249
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
6.906 Γ— 10⁹³(94-digit number)
69068515050913338993…38838588698120003251
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
1.381 Γ— 10⁹⁴(95-digit number)
13813703010182667798…77677177396240006499
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.381 Γ— 10⁹⁴(95-digit number)
13813703010182667798…77677177396240006501
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
2.762 Γ— 10⁹⁴(95-digit number)
27627406020365335597…55354354792480012999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.762 Γ— 10⁹⁴(95-digit number)
27627406020365335597…55354354792480013001
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
5.525 Γ— 10⁹⁴(95-digit number)
55254812040730671195…10708709584960025999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.525 Γ— 10⁹⁴(95-digit number)
55254812040730671195…10708709584960026001
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
1.105 Γ— 10⁹⁡(96-digit number)
11050962408146134239…21417419169920051999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.105 Γ— 10⁹⁡(96-digit number)
11050962408146134239…21417419169920052001
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
2.210 Γ— 10⁹⁡(96-digit number)
22101924816292268478…42834838339840103999
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 2272049

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 13ddab93e4afb2d42d060b37e80558d03e4a05aaaaf0c4e09606c899254ff7ed

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 #2,272,049 on Chainz β†—
Circulating Supply:57,888,225 XPMΒ·at block #6,830,496 Β· updates every 60s
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