XPM Prime Explorer symbol
XPMPrime Explorer

Block #3,039,723

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 2/5/2019, 9:25:41 AM Β· Difficulty 11.0196 Β· 3,803,173 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
e69e5db1a05cc5bc9163a24de533bf17038c01d1bbf8c686effa510fce3f8a50
View on Chainz β†—

Height

#3,039,723

Difficulty

11.019634

Transactions

2

Size

1.39 KB

Version

2

Bits

0b0506c4

Nonce

92,803,019

Timestamp

2/5/2019, 9:25:41 AM

Confirmations

3,803,173

Mined by

⛏️ P2SHAUhjokokGBrQRx2CtHWNPSvbj6k5m93PZR

Merkle Root

99cd7274c90f254eef0f13a3a1e306a1175aebdffbf7cc4839dfa832061ca773
Transactions (2)
Coinbase091c3bb5664cb2…48539f6505c45b
1 in β†’ 1 out8.2400 XPM109 B
AUhjokok…k5m93PZR
dc4ff8f05bbe2f…2af22beb1c556e
8 in β†’ 1 out1463.9551 XPM1.20 KB
ANeo8URS…WrC2zfLb
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.

2.306 Γ— 10⁹⁡(96-digit number)
23064445350536156309…40988478821588008959
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
2.306 Γ— 10⁹⁡(96-digit number)
23064445350536156309…40988478821588008959
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.306 Γ— 10⁹⁡(96-digit number)
23064445350536156309…40988478821588008961
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
4.612 Γ— 10⁹⁡(96-digit number)
46128890701072312619…81976957643176017919
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.612 Γ— 10⁹⁡(96-digit number)
46128890701072312619…81976957643176017921
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
9.225 Γ— 10⁹⁡(96-digit number)
92257781402144625238…63953915286352035839
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
9.225 Γ— 10⁹⁡(96-digit number)
92257781402144625238…63953915286352035841
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
1.845 Γ— 10⁹⁢(97-digit number)
18451556280428925047…27907830572704071679
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.845 Γ— 10⁹⁢(97-digit number)
18451556280428925047…27907830572704071681
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
3.690 Γ— 10⁹⁢(97-digit number)
36903112560857850095…55815661145408143359
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.690 Γ— 10⁹⁢(97-digit number)
36903112560857850095…55815661145408143361
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
7.380 Γ— 10⁹⁢(97-digit number)
73806225121715700190…11631322290816286719
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:57,987,516 XPMΒ·at block #6,842,895 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