XPM Prime Explorer symbol
XPMPrime Explorer

Block #663,526

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 8/5/2014, 8:36:07 AM Β· Difficulty 10.9577 Β· 6,161,765 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
46b22ab42d69c38a9cfc1f92036617786c19f012c368923bc61dcc15a550795f
View on Chainz β†—

Height

#663,526

Difficulty

10.957661

Transactions

2

Size

3.31 KB

Version

2

Bits

0af52949

Nonce

92,818,904

Timestamp

8/5/2014, 8:36:07 AM

Confirmations

6,161,765

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

ad15bdc76ae1ae6dc3b8fc48bf1aa67e1453943ec1f9f1118b97ec4527a4a146
Transactions (2)
Coinbase4576b014cae8f5…b80e9a206fd248
1 in β†’ 1 out8.3600 XPM116 B
ANSXnLY2…Sd25TjkD
46511b28a0b7e2…5ecfd693fec93a
21 in β†’ 2 out45.0306 XPM3.11 KB
AFuhi2tz…YXzYGhmFAV4Xnr9r…FWx4wj5F
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.

4.213 Γ— 10⁹⁢(97-digit number)
42130940840828735774…25787793142688183039
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
4.213 Γ— 10⁹⁢(97-digit number)
42130940840828735774…25787793142688183039
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.213 Γ— 10⁹⁢(97-digit number)
42130940840828735774…25787793142688183041
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
8.426 Γ— 10⁹⁢(97-digit number)
84261881681657471548…51575586285376366079
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
8.426 Γ— 10⁹⁢(97-digit number)
84261881681657471548…51575586285376366081
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
1.685 Γ— 10⁹⁷(98-digit number)
16852376336331494309…03151172570752732159
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.685 Γ— 10⁹⁷(98-digit number)
16852376336331494309…03151172570752732161
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
3.370 Γ— 10⁹⁷(98-digit number)
33704752672662988619…06302345141505464319
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.370 Γ— 10⁹⁷(98-digit number)
33704752672662988619…06302345141505464321
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
6.740 Γ— 10⁹⁷(98-digit number)
67409505345325977238…12604690283010928639
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
6.740 Γ— 10⁹⁷(98-digit number)
67409505345325977238…12604690283010928641
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
1.348 Γ— 10⁹⁸(99-digit number)
13481901069065195447…25209380566021857279
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,846,428 XPMΒ·at block #6,825,290 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