XPM Prime Explorer symbol
XPMPrime Explorer

Block #2,832,962

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 9/10/2018, 10:12:21 AM Β· Difficulty 11.7153 Β· 4,009,159 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
180129d4e3ea18ba93ab31d71e5967f78840ff56d6f8b54f09591bce7609a217
View on Chainz β†—

Height

#2,832,962

Difficulty

11.715293

Transactions

1

Size

201 B

Version

2

Bits

0bb71d6e

Nonce

1,806,085,785

Timestamp

9/10/2018, 10:12:21 AM

Confirmations

4,009,159

Mined by

⛏️ P2SHAedydznhzS8kvLPozLKPpH4a2EQ2xwnC6T

Merkle Root

0cdf53db001dbf038999b49a6745a0cf338c7b192c2d940c811ad96d7286984b
Transactions (1)
Coinbase0cdf53db001dbf…1ad96d7286984b
1 in β†’ 1 out7.2700 XPM110 B
Aedydznh…Q2xwnC6T
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.

4.713 Γ— 10⁹⁷(98-digit number)
47138972205883348652…01940596132683284479
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
4.713 Γ— 10⁹⁷(98-digit number)
47138972205883348652…01940596132683284479
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.713 Γ— 10⁹⁷(98-digit number)
47138972205883348652…01940596132683284481
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
9.427 Γ— 10⁹⁷(98-digit number)
94277944411766697305…03881192265366568959
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
9.427 Γ— 10⁹⁷(98-digit number)
94277944411766697305…03881192265366568961
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
1.885 Γ— 10⁹⁸(99-digit number)
18855588882353339461…07762384530733137919
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.885 Γ— 10⁹⁸(99-digit number)
18855588882353339461…07762384530733137921
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
3.771 Γ— 10⁹⁸(99-digit number)
37711177764706678922…15524769061466275839
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.771 Γ— 10⁹⁸(99-digit number)
37711177764706678922…15524769061466275841
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
7.542 Γ— 10⁹⁸(99-digit number)
75422355529413357844…31049538122932551679
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
7.542 Γ— 10⁹⁸(99-digit number)
75422355529413357844…31049538122932551681
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
1.508 Γ— 10⁹⁹(100-digit number)
15084471105882671568…62099076245865103359
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:57,981,355 XPMΒ·at block #6,842,120 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