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Home/Chain Registry/Block #2,634,405

Block #2,634,405

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 4/28/2018, 9:21:10 PM Β· Difficulty 11.2430 Β· 4,205,466 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
ecf012c535abf849d6e9089ab147b2bf1da066ee2ae03e926c23209b364fa726
View on Chainz β†—

Difficulty

11.242967

Transactions

1

Size

200 B

Version

2

Bits

0b3e3316

Nonce

479,890,294

Timestamp

4/28/2018, 9:21:10 PM

Confirmations

4,205,466

Merkle Root

3877b2051f69691d2ab4cfc086e9a28b03cc139958f14d5e78e3b81805c20af7
Transactions (1)
Coinbase3877b2051f6969…e3b81805c20af7
1 in β†’ 1 out7.9000 XPM110 B
Aduz7mVy…oN5XtZWt
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.

3.216 Γ— 10⁹⁡(96-digit number)
32168316807321465344…43474184014649144320
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
3.216 Γ— 10⁹⁡(96-digit number)
32168316807321465344…43474184014649144319
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.216 Γ— 10⁹⁡(96-digit number)
32168316807321465344…43474184014649144321
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
6.433 Γ— 10⁹⁡(96-digit number)
64336633614642930688…86948368029298288639
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.433 Γ— 10⁹⁡(96-digit number)
64336633614642930688…86948368029298288641
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
1.286 Γ— 10⁹⁢(97-digit number)
12867326722928586137…73896736058596577279
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.286 Γ— 10⁹⁢(97-digit number)
12867326722928586137…73896736058596577281
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
2.573 Γ— 10⁹⁢(97-digit number)
25734653445857172275…47793472117193154559
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.573 Γ— 10⁹⁢(97-digit number)
25734653445857172275…47793472117193154561
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
5.146 Γ— 10⁹⁢(97-digit number)
51469306891714344550…95586944234386309119
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.146 Γ— 10⁹⁢(97-digit number)
51469306891714344550…95586944234386309121
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
1.029 Γ— 10⁹⁷(98-digit number)
10293861378342868910…91173888468772618239
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 2634405

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 ecf012c535abf849d6e9089ab147b2bf1da066ee2ae03e926c23209b364fa726

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 #2,634,405 on Chainz β†—
Circulating Supply:57,963,268 XPMΒ·at block #6,839,870 Β· updates every 60s
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