XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #302,742

Block #302,742

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 12/9/2013, 11:57:15 PM Β· Difficulty 9.9928 Β· 6,522,199 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
2d6d1736fb9021fac329d2ab4df497a78dc20777a84314500628fb04977bf494
View on Chainz β†—

Height

#302,742

Difficulty

9.992799

Transactions

1

Size

208 B

Version

2

Bits

09fe2817

Nonce

9,320

Timestamp

12/9/2013, 11:57:15 PM

Confirmations

6,522,199

Merkle Root

ea689d9ad6f5a57cd131292d23b82636eab905492d8e4ae066ac904918565f56
Transactions (1)
Coinbaseea689d9ad6f5a5…ac904918565f56
1 in β†’ 1 out10.0000 XPM116 B
AbwWkWZt…kawDhufa
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.

8.652 Γ— 10⁹⁹(100-digit number)
86524967301985102381…77140306872114421760
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
8.652 Γ— 10⁹⁹(100-digit number)
86524967301985102381…77140306872114421759
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
8.652 Γ— 10⁹⁹(100-digit number)
86524967301985102381…77140306872114421761
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
1.730 Γ— 10¹⁰⁰(101-digit number)
17304993460397020476…54280613744228843519
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.730 Γ— 10¹⁰⁰(101-digit number)
17304993460397020476…54280613744228843521
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
3.460 Γ— 10¹⁰⁰(101-digit number)
34609986920794040952…08561227488457687039
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.460 Γ— 10¹⁰⁰(101-digit number)
34609986920794040952…08561227488457687041
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
6.921 Γ— 10¹⁰⁰(101-digit number)
69219973841588081904…17122454976915374079
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.921 Γ— 10¹⁰⁰(101-digit number)
69219973841588081904…17122454976915374081
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
1.384 Γ— 10¹⁰¹(102-digit number)
13843994768317616380…34244909953830748159
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.384 Γ— 10¹⁰¹(102-digit number)
13843994768317616380…34244909953830748161
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 302742

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 2d6d1736fb9021fac329d2ab4df497a78dc20777a84314500628fb04977bf494

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 #302,742 on Chainz β†—
Circulating Supply:57,843,604 XPMΒ·at block #6,824,940 Β· updates every 60s
xpmprime.info is a work in progress. If you enjoy using this service you can support this project with a Primecoin donation.
Privacy PolicyΒ·
AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

Cookie Preferences

We use cookies to enhance your experience. Some are essential for the site to function, while others help us understand how you use the site.

Β·Privacy Policy