XPM Prime Explorer symbol
XPMPrime Explorer

Block #1,967,892

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 2/3/2017, 10:38:03 PM Β· Difficulty 10.7524 Β· 4,870,524 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
e1d572566763c5a004a257f724ece271fd6a12639536d357a50557111d3e25c8
View on Chainz β†—

Height

#1,967,892

Difficulty

10.752412

Transactions

2

Size

1.28 KB

Version

2

Bits

0ac09e0f

Nonce

1,619,694,182

Timestamp

2/3/2017, 10:38:03 PM

Confirmations

4,870,524

Mined by

⛏️ P2SHAQHuqVkdpVebiiXtkyLYCp7AvZPP5B54T7

Merkle Root

31774cb20f4e196fc81dea281e1ff0a4d486a5eebd3913469d21ab4cdd1154c0
Transactions (2)
Coinbase60d6012bab3db0…b1648ed9e03023
1 in β†’ 1 out8.6600 XPM109 B
AQHuqVkd…PP5B54T7
8fa2d98b3ef383…fda01f7c3f1afc
7 in β†’ 2 out2.4290 XPM1.09 KB
AX6XP4sQ…Ffz69JA9AKnD9yiL…N4nmsrnx
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.

7.134 Γ— 10⁹³(94-digit number)
71344486101605709657…21521674453812867599
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
7.134 Γ— 10⁹³(94-digit number)
71344486101605709657…21521674453812867599
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
7.134 Γ— 10⁹³(94-digit number)
71344486101605709657…21521674453812867601
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
1.426 Γ— 10⁹⁴(95-digit number)
14268897220321141931…43043348907625735199
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.426 Γ— 10⁹⁴(95-digit number)
14268897220321141931…43043348907625735201
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
2.853 Γ— 10⁹⁴(95-digit number)
28537794440642283862…86086697815251470399
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.853 Γ— 10⁹⁴(95-digit number)
28537794440642283862…86086697815251470401
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
5.707 Γ— 10⁹⁴(95-digit number)
57075588881284567725…72173395630502940799
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.707 Γ— 10⁹⁴(95-digit number)
57075588881284567725…72173395630502940801
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
1.141 Γ— 10⁹⁡(96-digit number)
11415117776256913545…44346791261005881599
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.141 Γ— 10⁹⁡(96-digit number)
11415117776256913545…44346791261005881601
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:57,951,601 XPMΒ·at block #6,838,415 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