XPM Prime Explorer symbol
XPMPrime Explorer

Block #265,315

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 11/19/2013, 11:01:35 AM Β· Difficulty 9.9629 Β· 6,577,582 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
a606d5707e1dc01dc334a11b660b5ac8c0e7caa3a120d2229c0fb3233bebc185
View on Chainz β†—

Height

#265,315

Difficulty

9.962897

Transactions

2

Size

749 B

Version

2

Bits

09f6806a

Nonce

41,845

Timestamp

11/19/2013, 11:01:35 AM

Confirmations

6,577,582

Mined by

⛏️ P2SHAKcbk49N7DP3nse7MJr3Ed6rZiGJbKa7j1

Merkle Root

8e5b188ee68c48d9d19715a4ca8e08b6a915c2d83997b744886e669f1315c4fc
Transactions (2)
Coinbase5d83342ab18ed9…d23f98cd28a7f1
1 in β†’ 2 out10.0700 XPM136 B
AKcbk49N…GJbKa7j1ASNt3cJa…L5zCqAYM
7de58698a3835b…e126a36d6ff9de
3 in β†’ 2 out2.5126 XPM522 B
AFvgyX7A…1nBm59dsATjbP3zK…HdN6otNZ
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.

1.174 Γ— 10⁹⁷(98-digit number)
11743257690819724904…24124672185420922879
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
1.174 Γ— 10⁹⁷(98-digit number)
11743257690819724904…24124672185420922879
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.174 Γ— 10⁹⁷(98-digit number)
11743257690819724904…24124672185420922881
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
2.348 Γ— 10⁹⁷(98-digit number)
23486515381639449808…48249344370841845759
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.348 Γ— 10⁹⁷(98-digit number)
23486515381639449808…48249344370841845761
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
4.697 Γ— 10⁹⁷(98-digit number)
46973030763278899617…96498688741683691519
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.697 Γ— 10⁹⁷(98-digit number)
46973030763278899617…96498688741683691521
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
9.394 Γ— 10⁹⁷(98-digit number)
93946061526557799234…92997377483367383039
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
9.394 Γ— 10⁹⁷(98-digit number)
93946061526557799234…92997377483367383041
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
1.878 Γ— 10⁹⁸(99-digit number)
18789212305311559846…85994754966734766079
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:57,987,524 XPMΒ·at block #6,842,896 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