XPM Prime Explorer symbol
XPMPrime Explorer

Block #167,853

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/16/2013, 9:48:29 PM Β· Difficulty 9.8682 Β· 6,675,144 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
cecbc43b5b55143d2ac11da10a8ed546e5d4be306250451a4cffcbf6a6803a79
View on Chainz β†—

Height

#167,853

Difficulty

9.868159

Transactions

1

Size

199 B

Version

2

Bits

09de3fa7

Nonce

49,787

Timestamp

9/16/2013, 9:48:29 PM

Confirmations

6,675,144

Mined by

⛏️ P2SHAYAZW9zaEPqgug8XGBA3iA2Nf3da8AvwiQ

Merkle Root

88ce6b13d257045ba95b149ce1829a4ccb9d2a6489b8923b656b770ca5c7f0d4
Transactions (1)
Coinbase88ce6b13d25704…6b770ca5c7f0d4
1 in β†’ 1 out10.2500 XPM109 B
AYAZW9za…da8AvwiQ
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.

4.527 Γ— 10⁹⁡(96-digit number)
45270468943058883537…53943504744423770479
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
4.527 Γ— 10⁹⁡(96-digit number)
45270468943058883537…53943504744423770479
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.527 Γ— 10⁹⁡(96-digit number)
45270468943058883537…53943504744423770481
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
9.054 Γ— 10⁹⁡(96-digit number)
90540937886117767075…07887009488847540959
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
9.054 Γ— 10⁹⁡(96-digit number)
90540937886117767075…07887009488847540961
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
1.810 Γ— 10⁹⁢(97-digit number)
18108187577223553415…15774018977695081919
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.810 Γ— 10⁹⁢(97-digit number)
18108187577223553415…15774018977695081921
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
3.621 Γ— 10⁹⁢(97-digit number)
36216375154447106830…31548037955390163839
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.621 Γ— 10⁹⁢(97-digit number)
36216375154447106830…31548037955390163841
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
7.243 Γ— 10⁹⁢(97-digit number)
72432750308894213660…63096075910780327679
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:57,988,331 XPMΒ·at block #6,842,996 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