XPM Prime Explorer symbol
XPMPrime Explorer

Block #716,254

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/11/2014, 11:47:24 AM Β· Difficulty 10.9529 Β· 6,108,961 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
a68fa0633cc05e6e39df957a6642c6d50f5eb5f68a50062236c967df422a08f9
View on Chainz β†—

Height

#716,254

Difficulty

10.952934

Transactions

2

Size

6.46 KB

Version

2

Bits

0af3f377

Nonce

196,375,738

Timestamp

9/11/2014, 11:47:24 AM

Confirmations

6,108,961

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

ddade37e2c55e89a3765eea3c4d3571b5d632bdb776ad875cb2683cc20335dbd
Transactions (2)
Coinbase176b551f4eb9da…ec6484e1196f11
1 in β†’ 1 out8.3900 XPM116 B
ANSXnLY2…Sd25TjkD
da5cccdc786d3a…5f832077334244
43 in β†’ 1 out196.2702 XPM6.26 KB
AQE35QmL…E2W2VG4x
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.

3.420 Γ— 10⁹⁢(97-digit number)
34201549626654195336…09787384947377635839
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
3.420 Γ— 10⁹⁢(97-digit number)
34201549626654195336…09787384947377635839
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.420 Γ— 10⁹⁢(97-digit number)
34201549626654195336…09787384947377635841
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
6.840 Γ— 10⁹⁢(97-digit number)
68403099253308390673…19574769894755271679
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.840 Γ— 10⁹⁢(97-digit number)
68403099253308390673…19574769894755271681
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
1.368 Γ— 10⁹⁷(98-digit number)
13680619850661678134…39149539789510543359
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.368 Γ— 10⁹⁷(98-digit number)
13680619850661678134…39149539789510543361
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
2.736 Γ— 10⁹⁷(98-digit number)
27361239701323356269…78299079579021086719
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.736 Γ— 10⁹⁷(98-digit number)
27361239701323356269…78299079579021086721
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
5.472 Γ— 10⁹⁷(98-digit number)
54722479402646712538…56598159158042173439
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.472 Γ— 10⁹⁷(98-digit number)
54722479402646712538…56598159158042173441
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,845,814 XPMΒ·at block #6,825,214 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