XPM Prime Explorer symbol
XPMPrime Explorer

Block #2,826,251

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 9/5/2018, 7:45:05 PM Β· Difficulty 11.7103 Β· 4,015,994 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
adf6609bce32fe226e29ceb03ad3cf6f89aad4897a175e25952edb44c1467b7f
View on Chainz β†—

Height

#2,826,251

Difficulty

11.710341

Transactions

1

Size

200 B

Version

2

Bits

0bb5d8ed

Nonce

1,994,588,962

Timestamp

9/5/2018, 7:45:05 PM

Confirmations

4,015,994

Mined by

⛏️ P2SHATLVKcXATXcfoTA32Ab6KuUZjdp5fWBFxZ

Merkle Root

7bfbd85a0883ec15cd0e4fdd6a33342aca0ddf94256ef22b155478e4ec24f385
Transactions (1)
Coinbase7bfbd85a0883ec…5478e4ec24f385
1 in β†’ 1 out7.2800 XPM110 B
ATLVKcXA…p5fWBFxZ
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.

1.920 Γ— 10⁹⁡(96-digit number)
19200563289937820056…28458932133215193759
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
1.920 Γ— 10⁹⁡(96-digit number)
19200563289937820056…28458932133215193759
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.920 Γ— 10⁹⁡(96-digit number)
19200563289937820056…28458932133215193761
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
3.840 Γ— 10⁹⁡(96-digit number)
38401126579875640112…56917864266430387519
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.840 Γ— 10⁹⁡(96-digit number)
38401126579875640112…56917864266430387521
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
7.680 Γ— 10⁹⁡(96-digit number)
76802253159751280225…13835728532860775039
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
7.680 Γ— 10⁹⁡(96-digit number)
76802253159751280225…13835728532860775041
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
1.536 Γ— 10⁹⁢(97-digit number)
15360450631950256045…27671457065721550079
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.536 Γ— 10⁹⁢(97-digit number)
15360450631950256045…27671457065721550081
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
3.072 Γ— 10⁹⁢(97-digit number)
30720901263900512090…55342914131443100159
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.072 Γ— 10⁹⁢(97-digit number)
30720901263900512090…55342914131443100161
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
6.144 Γ— 10⁹⁢(97-digit number)
61441802527801024180…10685828262886200319
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:57,982,358 XPMΒ·at block #6,842,244 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