XPM Prime Explorer symbol
XPMPrime Explorer

Block #2,282,372

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 9/4/2017, 5:21:13 PM Β· Difficulty 10.9557 Β· 4,562,615 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
5d18e29cfadc59e64c50bc2d125e2a8aabac602a0d41eebafb3e001a4b0aee06
View on Chainz β†—

Height

#2,282,372

Difficulty

10.955667

Transactions

1

Size

243 B

Version

2

Bits

0af4a699

Nonce

972,284,191

Timestamp

9/4/2017, 5:21:13 PM

Confirmations

4,562,615

Mined by

⛏️ P2SHARNe3C8DxSRf1CqKsGiVNkhAx4KfGUT8YN

Merkle Root

70c3ee41ae0bf306efecef692c29dd68d151666a4e0abbf632ebd70f97995275
Transactions (1)
Coinbase70c3ee41ae0bf3…ebd70f97995275
1 in β†’ 2 out8.3200 XPM152 B
ARNe3C8D…KfGUT8YNAXbk7f7A…Tx7JECPG
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.

1.124 Γ— 10⁹⁢(97-digit number)
11246778783506594585…29429422226962415359
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
1.124 Γ— 10⁹⁢(97-digit number)
11246778783506594585…29429422226962415359
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.124 Γ— 10⁹⁢(97-digit number)
11246778783506594585…29429422226962415361
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
2.249 Γ— 10⁹⁢(97-digit number)
22493557567013189170…58858844453924830719
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.249 Γ— 10⁹⁢(97-digit number)
22493557567013189170…58858844453924830721
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
4.498 Γ— 10⁹⁢(97-digit number)
44987115134026378340…17717688907849661439
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.498 Γ— 10⁹⁢(97-digit number)
44987115134026378340…17717688907849661441
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
8.997 Γ— 10⁹⁢(97-digit number)
89974230268052756681…35435377815699322879
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
8.997 Γ— 10⁹⁢(97-digit number)
89974230268052756681…35435377815699322881
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
1.799 Γ— 10⁹⁷(98-digit number)
17994846053610551336…70870755631398645759
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.799 Γ— 10⁹⁷(98-digit number)
17994846053610551336…70870755631398645761
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
3.598 Γ— 10⁹⁷(98-digit number)
35989692107221102672…41741511262797291519
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:58,004,315 XPMΒ·at block #6,844,986 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