XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #1,208,984

Block #1,208,984

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 8/26/2015, 7:46:05 AM Β· Difficulty 10.7657 Β· 5,615,945 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
8d6d30984f125b5feab1ed9a259cec3e10421c3df4d19bc20bca886e9ebcda23
View on Chainz β†—

Difficulty

10.765736

Transactions

1

Size

207 B

Version

2

Bits

0ac40744

Nonce

1,143,585,384

Timestamp

8/26/2015, 7:46:05 AM

Confirmations

5,615,945

Merkle Root

c34f4b0076954d164e3dd980100d4075071c9e731e60c7d16961d668714754a1
Transactions (1)
Coinbasec34f4b0076954d…61d668714754a1
1 in β†’ 1 out8.6100 XPM116 B
AJCEY9yy…tg97E6zm
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.

7.561 Γ— 10⁹⁢(97-digit number)
75610354312733993155…65350510775207676160
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
7.561 Γ— 10⁹⁢(97-digit number)
75610354312733993155…65350510775207676159
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
7.561 Γ— 10⁹⁢(97-digit number)
75610354312733993155…65350510775207676161
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
1.512 Γ— 10⁹⁷(98-digit number)
15122070862546798631…30701021550415352319
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.512 Γ— 10⁹⁷(98-digit number)
15122070862546798631…30701021550415352321
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
3.024 Γ— 10⁹⁷(98-digit number)
30244141725093597262…61402043100830704639
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.024 Γ— 10⁹⁷(98-digit number)
30244141725093597262…61402043100830704641
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
6.048 Γ— 10⁹⁷(98-digit number)
60488283450187194524…22804086201661409279
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.048 Γ— 10⁹⁷(98-digit number)
60488283450187194524…22804086201661409281
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
1.209 Γ— 10⁹⁸(99-digit number)
12097656690037438904…45608172403322818559
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.209 Γ— 10⁹⁸(99-digit number)
12097656690037438904…45608172403322818561
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 1208984

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 8d6d30984f125b5feab1ed9a259cec3e10421c3df4d19bc20bca886e9ebcda23

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 #1,208,984 on Chainz β†—
Circulating Supply:57,843,508 XPMΒ·at block #6,824,928 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