XPM Prime Explorer symbol
XPMPrime Explorer

Block #176,612

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/23/2013, 1:46:06 AM Β· Difficulty 9.8656 Β· 6,629,830 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
a10081662caf47809980e2f2b413a3d17696641c09ef1cfb5a4098573225b24a
View on Chainz β†—

Height

#176,612

Difficulty

9.865597

Transactions

2

Size

697 B

Version

2

Bits

09dd97bd

Nonce

22,633

Timestamp

9/23/2013, 1:46:06 AM

Confirmations

6,629,830

Mined by

⛏️ P2SHARCk398gnEDgEgLqhKzA7CPj9DztdKPSnk

Merkle Root

3175aa2b8ef748b04b12acc5df2e8f6af225de8d220a22cd31d6b89061da8d8d
Transactions (2)
Coinbased6a51ff8c90025…09ea3a7f4d0a96
1 in β†’ 1 out10.2700 XPM109 B
ARCk398g…ztdKPSnk
8596a582f882cb…3c6bc1ea52b3e0
4 in β†’ 1 out41.0200 XPM498 B
AU63Ubwp…RaoT2ZVk
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.

1.659 Γ— 10⁹⁴(95-digit number)
16599493955067764712…82121734643855755519
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
1.659 Γ— 10⁹⁴(95-digit number)
16599493955067764712…82121734643855755519
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.659 Γ— 10⁹⁴(95-digit number)
16599493955067764712…82121734643855755521
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
3.319 Γ— 10⁹⁴(95-digit number)
33198987910135529424…64243469287711511039
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.319 Γ— 10⁹⁴(95-digit number)
33198987910135529424…64243469287711511041
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
6.639 Γ— 10⁹⁴(95-digit number)
66397975820271058849…28486938575423022079
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.639 Γ— 10⁹⁴(95-digit number)
66397975820271058849…28486938575423022081
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
1.327 Γ— 10⁹⁡(96-digit number)
13279595164054211769…56973877150846044159
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.327 Γ— 10⁹⁡(96-digit number)
13279595164054211769…56973877150846044161
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
2.655 Γ— 10⁹⁡(96-digit number)
26559190328108423539…13947754301692088319
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:57,695,625 XPMΒ·at block #6,806,441 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.
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