XPM Prime Explorer symbol
XPMPrime Explorer

Block #163,018

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/13/2013, 5:09:19 PM Β· Difficulty 9.8616 Β· 6,653,812 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
813ac905da979e06f895270d04f72216c01e2e090313982e8262a7a4e9e2ae85
View on Chainz β†—

Height

#163,018

Difficulty

9.861645

Transactions

1

Size

199 B

Version

2

Bits

09dc94bd

Nonce

72,580

Timestamp

9/13/2013, 5:09:19 PM

Confirmations

6,653,812

Mined by

⛏️ P2SHAWbm4AWfhyZEMkdPYLMs4FyYdBzNGrUw91

Merkle Root

6a93e29c7a59fdd8cb8d34679826e8757606f1dcf1fb136bea9a78e2e985ab64
Transactions (1)
Coinbase6a93e29c7a59fd…9a78e2e985ab64
1 in β†’ 1 out10.2700 XPM109 B
AWbm4AWf…zNGrUw91
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.

1.734 Γ— 10⁹⁡(96-digit number)
17340142316383689529…85550028241666298719
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
1.734 Γ— 10⁹⁡(96-digit number)
17340142316383689529…85550028241666298719
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.734 Γ— 10⁹⁡(96-digit number)
17340142316383689529…85550028241666298721
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
3.468 Γ— 10⁹⁡(96-digit number)
34680284632767379058…71100056483332597439
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.468 Γ— 10⁹⁡(96-digit number)
34680284632767379058…71100056483332597441
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
6.936 Γ— 10⁹⁡(96-digit number)
69360569265534758117…42200112966665194879
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.936 Γ— 10⁹⁡(96-digit number)
69360569265534758117…42200112966665194881
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
1.387 Γ— 10⁹⁢(97-digit number)
13872113853106951623…84400225933330389759
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.387 Γ— 10⁹⁢(97-digit number)
13872113853106951623…84400225933330389761
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
2.774 Γ— 10⁹⁢(97-digit number)
27744227706213903246…68800451866660779519
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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.

β˜…β˜†β˜†β˜†β˜†
Rarity
CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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
Cross-reference on Chainz Explorer
Circulating Supply:57,778,680 XPMΒ·at block #6,816,829 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