XPM Prime Explorer symbol
XPMPrime Explorer

Block #2,947,345

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 12/1/2018, 1:27:15 PM Β· Difficulty 11.3905 Β· 3,879,891 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
becf366f6302680b71ba7a5606e7f25fe9dce3fadf2c195469c2728b2fc043a6
View on Chainz β†—

Height

#2,947,345

Difficulty

11.390494

Transactions

2

Size

4.46 KB

Version

2

Bits

0b63f766

Nonce

53,767,304

Timestamp

12/1/2018, 1:27:15 PM

Confirmations

3,879,891

Mined by

⛏️ P2SHAbXwmGxDc5ZxwPwgT1QckjRUmF4XXYP765

Merkle Root

7762c88bfa2b486e2223662f630cb03dcf2534aa260f8de47b7e102610d3c057
Transactions (2)
Coinbaseece35bbe823b95…70e014d7e5785f
1 in β†’ 1 out7.7400 XPM110 B
AbXwmGxD…4XXYP765
ef54d632ceb5c5…6042d73674fea8
29 in β†’ 2 out7653.2528 XPM4.27 KB
AedZFv4c…Aqj1LPPPAbfHPQRP…cc1QCTYa
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.

2.522 Γ— 10⁹⁡(96-digit number)
25221284238819916570…56965953632231501999
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
2.522 Γ— 10⁹⁡(96-digit number)
25221284238819916570…56965953632231501999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.522 Γ— 10⁹⁡(96-digit number)
25221284238819916570…56965953632231502001
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
5.044 Γ— 10⁹⁡(96-digit number)
50442568477639833140…13931907264463003999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.044 Γ— 10⁹⁡(96-digit number)
50442568477639833140…13931907264463004001
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
1.008 Γ— 10⁹⁢(97-digit number)
10088513695527966628…27863814528926007999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.008 Γ— 10⁹⁢(97-digit number)
10088513695527966628…27863814528926008001
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
2.017 Γ— 10⁹⁢(97-digit number)
20177027391055933256…55727629057852015999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.017 Γ— 10⁹⁢(97-digit number)
20177027391055933256…55727629057852016001
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
4.035 Γ— 10⁹⁢(97-digit number)
40354054782111866512…11455258115704031999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.035 Γ— 10⁹⁢(97-digit number)
40354054782111866512…11455258115704032001
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
8.070 Γ— 10⁹⁢(97-digit number)
80708109564223733025…22910516231408063999
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:57,861,989 XPMΒ·at block #6,827,235 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