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Block #2,872,303

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 10/8/2018, 7:44:09 AM Β· Difficulty 11.6658 Β· 3,968,173 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
86852685dcb2dc6622da658659862181612394f61dd838510c0ea689fcbb6db7
View on Chainz β†—

Height

#2,872,303

Difficulty

11.665826

Transactions

1

Size

201 B

Version

2

Bits

0baa7391

Nonce

1,362,407,321

Timestamp

10/8/2018, 7:44:09 AM

Confirmations

3,968,173

Mined by

⛏️ P2SHAaCyJex3B3jquqmmodkSFoWH13bJDMpidi

Merkle Root

5423e38fb9537d739e3e744bfc7ea9713bf8dc155069996854c788082f2b1b20
Transactions (1)
Coinbase5423e38fb9537d…c788082f2b1b20
1 in β†’ 1 out7.3400 XPM110 B
AaCyJex3…bJDMpidi
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.

5.458 Γ— 10⁹⁢(97-digit number)
54582886289277608268…43735761406755143679
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
5.458 Γ— 10⁹⁢(97-digit number)
54582886289277608268…43735761406755143679
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.458 Γ— 10⁹⁢(97-digit number)
54582886289277608268…43735761406755143681
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
1.091 Γ— 10⁹⁷(98-digit number)
10916577257855521653…87471522813510287359
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.091 Γ— 10⁹⁷(98-digit number)
10916577257855521653…87471522813510287361
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
2.183 Γ— 10⁹⁷(98-digit number)
21833154515711043307…74943045627020574719
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.183 Γ— 10⁹⁷(98-digit number)
21833154515711043307…74943045627020574721
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
4.366 Γ— 10⁹⁷(98-digit number)
43666309031422086615…49886091254041149439
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.366 Γ— 10⁹⁷(98-digit number)
43666309031422086615…49886091254041149441
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
8.733 Γ— 10⁹⁷(98-digit number)
87332618062844173230…99772182508082298879
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
8.733 Γ— 10⁹⁷(98-digit number)
87332618062844173230…99772182508082298881
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
1.746 Γ— 10⁹⁸(99-digit number)
17466523612568834646…99544365016164597759
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:57,968,139 XPMΒ·at block #6,840,475 Β· updates every 60s
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