XPM Prime Explorer symbol
XPMPrime Explorer

Block #1,477,430

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 2/29/2016, 5:41:59 PM Β· Difficulty 10.7037 Β· 5,367,759 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
dad2844a262649e22708a3a8b06c5d15423e32af039e91a96204df83ce10e2d0
View on Chainz β†—

Height

#1,477,430

Difficulty

10.703663

Transactions

1

Size

243 B

Version

2

Bits

0ab42343

Nonce

977,899,721

Timestamp

2/29/2016, 5:41:59 PM

Confirmations

5,367,759

Mined by

⛏️ P2SHAdwKJkgSub5gUckyBUnSUJCm23L2zsc2ej

Merkle Root

f1ee4990f0ec69dc6eae736f3330c580c594235fc1b117fa5afdf44b94ab37ee
Transactions (1)
Coinbasef1ee4990f0ec69…fdf44b94ab37ee
1 in β†’ 2 out8.7100 XPM152 B
AdwKJkgS…L2zsc2ejALPu3s2c…EJXLjVFh
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.

9.189 Γ— 10⁹⁢(97-digit number)
91891602122039027979…54090949822219032319
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
9.189 Γ— 10⁹⁢(97-digit number)
91891602122039027979…54090949822219032319
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
9.189 Γ— 10⁹⁢(97-digit number)
91891602122039027979…54090949822219032321
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
1.837 Γ— 10⁹⁷(98-digit number)
18378320424407805595…08181899644438064639
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.837 Γ— 10⁹⁷(98-digit number)
18378320424407805595…08181899644438064641
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
3.675 Γ— 10⁹⁷(98-digit number)
36756640848815611191…16363799288876129279
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.675 Γ— 10⁹⁷(98-digit number)
36756640848815611191…16363799288876129281
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
7.351 Γ— 10⁹⁷(98-digit number)
73513281697631222383…32727598577752258559
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
7.351 Γ— 10⁹⁷(98-digit number)
73513281697631222383…32727598577752258561
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
1.470 Γ— 10⁹⁸(99-digit number)
14702656339526244476…65455197155504517119
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.470 Γ— 10⁹⁸(99-digit number)
14702656339526244476…65455197155504517121
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:58,005,942 XPMΒ·at block #6,845,188 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