XPM Prime Explorer symbol
XPMPrime Explorer

Block #2,696,723

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 6/8/2018, 8:30:58 AM Β· Difficulty 11.6633 Β· 4,136,894 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
d729198060ff36c899b29b5a74a09d6782f3c0649008ae445eadf4720cae8770
View on Chainz β†—

Height

#2,696,723

Difficulty

11.663280

Transactions

2

Size

541 B

Version

2

Bits

0ba9ccb2

Nonce

250,646,663

Timestamp

6/8/2018, 8:30:58 AM

Confirmations

4,136,894

Mined by

⛏️ P2SHAP3ZAwjaZuupyG8HGKoxCWNjA6VoGEp6cW

Merkle Root

aa6011836c668eb239ba00f7bf0f8f12ab3057d0aa01501f5c18691f9cb9369e
Transactions (2)
Coinbase3a4930948a45da…6f6d6974496d36
1 in β†’ 1 out7.3500 XPM110 B
AP3ZAwja…VoGEp6cW
5f124ff5264d10…1c388954dc036f
2 in β†’ 2 out11.9400 XPM342 B
AMZTvt4A…avM6d4EKASQ5SGd2…Bk3wNRzc
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.

6.117 Γ— 10⁹²(93-digit number)
61179833875172673407…15588173121559831679
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
6.117 Γ— 10⁹²(93-digit number)
61179833875172673407…15588173121559831679
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
6.117 Γ— 10⁹²(93-digit number)
61179833875172673407…15588173121559831681
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
1.223 Γ— 10⁹³(94-digit number)
12235966775034534681…31176346243119663359
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.223 Γ— 10⁹³(94-digit number)
12235966775034534681…31176346243119663361
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
2.447 Γ— 10⁹³(94-digit number)
24471933550069069362…62352692486239326719
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.447 Γ— 10⁹³(94-digit number)
24471933550069069362…62352692486239326721
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
4.894 Γ— 10⁹³(94-digit number)
48943867100138138725…24705384972478653439
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.894 Γ— 10⁹³(94-digit number)
48943867100138138725…24705384972478653441
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
9.788 Γ— 10⁹³(94-digit number)
97887734200276277451…49410769944957306879
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
9.788 Γ— 10⁹³(94-digit number)
97887734200276277451…49410769944957306881
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
1.957 Γ— 10⁹⁴(95-digit number)
19577546840055255490…98821539889914613759
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:57,913,146 XPMΒ·at block #6,833,616 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