XPM Prime Explorer symbol
XPMPrime Explorer

Block #1,683,286

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/21/2016, 1:37:03 PM Β· Difficulty 10.7217 Β· 5,126,336 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
91fff6b5b38e9f1ca4ee469d04310f468861b28ecf4f5089982e5437511871f5
View on Chainz β†—

Height

#1,683,286

Difficulty

10.721655

Transactions

2

Size

29.85 KB

Version

2

Bits

0ab8be5c

Nonce

206,148,527

Timestamp

7/21/2016, 1:37:03 PM

Confirmations

5,126,336

Mined by

⛏️ P2SHAen4J3JvxC9VhcZBAbA4AQysgqQUpLM9Zs

Merkle Root

187865ed2a913bb0b572eca5c418ebfed8adaa535b7f07383c28c3d579c85956
Transactions (2)
Coinbase66ed7db3acb47d…cf8f558e6c55f5
1 in β†’ 1 out9.0000 XPM109 B
Aen4J3Jv…QUpLM9Zs
5b1957ab392b6e…d0590772282966
205 in β†’ 1 out17.2270 XPM29.66 KB
AGyiGjWR…yy2Gk1HV
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.

8.142 Γ— 10⁹⁡(96-digit number)
81421482096087078105…62972032967547015039
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
8.142 Γ— 10⁹⁡(96-digit number)
81421482096087078105…62972032967547015039
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
8.142 Γ— 10⁹⁡(96-digit number)
81421482096087078105…62972032967547015041
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
1.628 Γ— 10⁹⁢(97-digit number)
16284296419217415621…25944065935094030079
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.628 Γ— 10⁹⁢(97-digit number)
16284296419217415621…25944065935094030081
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
3.256 Γ— 10⁹⁢(97-digit number)
32568592838434831242…51888131870188060159
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.256 Γ— 10⁹⁢(97-digit number)
32568592838434831242…51888131870188060161
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
6.513 Γ— 10⁹⁢(97-digit number)
65137185676869662484…03776263740376120319
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.513 Γ— 10⁹⁢(97-digit number)
65137185676869662484…03776263740376120321
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
1.302 Γ— 10⁹⁷(98-digit number)
13027437135373932496…07552527480752240639
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.302 Γ— 10⁹⁷(98-digit number)
13027437135373932496…07552527480752240641
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:57,721,054 XPMΒ·at block #6,809,621 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.
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