XPM Prime Explorer symbol
XPMPrime Explorer

Block #2,099,566

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 5/4/2017, 2:09:38 PM Β· Difficulty 10.8562 Β· 4,741,682 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
52d195934cdc2b992953d35c1e24e9238b657f381240fec2e262bc6ff3195b36
View on Chainz β†—

Height

#2,099,566

Difficulty

10.856179

Transactions

2

Size

2.70 KB

Version

2

Bits

0adb2e8e

Nonce

1,035,416,541

Timestamp

5/4/2017, 2:09:38 PM

Confirmations

4,741,682

Mined by

⛏️ P2SHAQQVwBKvvUopXqQgLzFm2nw3aSw7CpE7Th

Merkle Root

3372a738051d0d469b97fc80d205f5f69ff58ad81e08753d97c91e2ff4fca552
Transactions (2)
Coinbase7a526e61067eb2…4669860fe89ab9
1 in β†’ 1 out8.5000 XPM109 B
AQQVwBKv…w7CpE7Th
5e580b35f6fba8…50314cda3c294e
17 in β†’ 1 out399.9900 XPM2.51 KB
AZAUpPRK…y6qkZdaT
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.

5.948 Γ— 10⁹⁷(98-digit number)
59487971842397399532…29487888679747911679
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
5.948 Γ— 10⁹⁷(98-digit number)
59487971842397399532…29487888679747911679
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.948 Γ— 10⁹⁷(98-digit number)
59487971842397399532…29487888679747911681
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
1.189 Γ— 10⁹⁸(99-digit number)
11897594368479479906…58975777359495823359
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.189 Γ— 10⁹⁸(99-digit number)
11897594368479479906…58975777359495823361
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
2.379 Γ— 10⁹⁸(99-digit number)
23795188736958959813…17951554718991646719
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.379 Γ— 10⁹⁸(99-digit number)
23795188736958959813…17951554718991646721
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
4.759 Γ— 10⁹⁸(99-digit number)
47590377473917919626…35903109437983293439
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.759 Γ— 10⁹⁸(99-digit number)
47590377473917919626…35903109437983293441
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
9.518 Γ— 10⁹⁸(99-digit number)
95180754947835839252…71806218875966586879
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
9.518 Γ— 10⁹⁸(99-digit number)
95180754947835839252…71806218875966586881
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:57,974,346 XPMΒ·at block #6,841,247 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