XPM Prime Explorer symbol
XPMPrime Explorer

Block #1,534,655

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 4/10/2016, 9:39:05 AM Β· Difficulty 10.6170 Β· 5,283,122 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
dde0cfecf067b69872b3020cf4523178a4a74458999c039fd69b17dedf16e02f
View on Chainz β†—

Height

#1,534,655

Difficulty

10.617039

Transactions

2

Size

7.61 KB

Version

2

Bits

0a9df645

Nonce

461,432,021

Timestamp

4/10/2016, 9:39:05 AM

Confirmations

5,283,122

Mined by

⛏️ P2SHAeGUjCY3AHiUENyXoNcSENpdw2HP8mTe7k

Merkle Root

b35385c5ede86d66944f1316ba1a559ab3136a4a41e2b2668ae296c903347878
Transactions (2)
Coinbasea8f1766f3decd7…43929a21fa73d5
1 in β†’ 1 out8.9400 XPM109 B
AeGUjCY3…HP8mTe7k
d691d36be9500c…bfe3590cc06072
51 in β†’ 1 out3010.8226 XPM7.42 KB
ATb9jtWZ…vdDqhjd6
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.

4.360 Γ— 10⁹³(94-digit number)
43604953272622111254…45725857034961626499
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
4.360 Γ— 10⁹³(94-digit number)
43604953272622111254…45725857034961626499
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.360 Γ— 10⁹³(94-digit number)
43604953272622111254…45725857034961626501
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
8.720 Γ— 10⁹³(94-digit number)
87209906545244222509…91451714069923252999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
8.720 Γ— 10⁹³(94-digit number)
87209906545244222509…91451714069923253001
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
1.744 Γ— 10⁹⁴(95-digit number)
17441981309048844501…82903428139846505999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.744 Γ— 10⁹⁴(95-digit number)
17441981309048844501…82903428139846506001
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
3.488 Γ— 10⁹⁴(95-digit number)
34883962618097689003…65806856279693011999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.488 Γ— 10⁹⁴(95-digit number)
34883962618097689003…65806856279693012001
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
6.976 Γ— 10⁹⁴(95-digit number)
69767925236195378007…31613712559386023999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
6.976 Γ— 10⁹⁴(95-digit number)
69767925236195378007…31613712559386024001
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
1.395 Γ— 10⁹⁡(96-digit number)
13953585047239075601…63227425118772047999
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:57,786,274 XPMΒ·at block #6,817,776 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