XPM Prime Explorer symbol
XPMPrime Explorer

Block #3,033,921

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 2/1/2019, 7:34:23 AM Β· Difficulty 11.0331 Β· 3,811,105 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
69d53e98dd614bca06900233f4d4ff73105fa4ca27511e91e4abea626879369f
View on Chainz β†—

Height

#3,033,921

Difficulty

11.033143

Transactions

1

Size

199 B

Version

2

Bits

0b087c07

Nonce

1,035,838,604

Timestamp

2/1/2019, 7:34:23 AM

Confirmations

3,811,105

Mined by

⛏️ P2SHAUhjokokGBrQRx2CtHWNPSvbj6k5m93PZR

Merkle Root

10f674695a2bc86f2330a085c9b31731f42afaf3e8566e9003da39d0b7a2f012
Transactions (1)
Coinbase10f674695a2bc8…da39d0b7a2f012
1 in β†’ 1 out8.2000 XPM110 B
AUhjokok…k5m93PZR
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.

1.679 Γ— 10⁹³(94-digit number)
16796366766089696716…70145389851177532809
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
1.679 Γ— 10⁹³(94-digit number)
16796366766089696716…70145389851177532809
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.679 Γ— 10⁹³(94-digit number)
16796366766089696716…70145389851177532811
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
3.359 Γ— 10⁹³(94-digit number)
33592733532179393433…40290779702355065619
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.359 Γ— 10⁹³(94-digit number)
33592733532179393433…40290779702355065621
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
6.718 Γ— 10⁹³(94-digit number)
67185467064358786866…80581559404710131239
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.718 Γ— 10⁹³(94-digit number)
67185467064358786866…80581559404710131241
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
1.343 Γ— 10⁹⁴(95-digit number)
13437093412871757373…61163118809420262479
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.343 Γ— 10⁹⁴(95-digit number)
13437093412871757373…61163118809420262481
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
2.687 Γ— 10⁹⁴(95-digit number)
26874186825743514746…22326237618840524959
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.687 Γ— 10⁹⁴(95-digit number)
26874186825743514746…22326237618840524961
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
5.374 Γ— 10⁹⁴(95-digit number)
53748373651487029493…44652475237681049919
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:58,004,633 XPMΒ·at block #6,845,025 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