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Block #2,638,449

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 4/30/2018, 7:08:06 AM Β· Difficulty 11.4928 Β· 4,201,426 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
1e1f94d3c904cabf6c0a3a13659441076e605f61d491e8dab42b814a7c2107ee
View on Chainz β†—

Height

#2,638,449

Difficulty

11.492761

Transactions

1

Size

201 B

Version

2

Bits

0b7e259e

Nonce

113,168,073

Timestamp

4/30/2018, 7:08:06 AM

Confirmations

4,201,426

Mined by

⛏️ P2SHAdyAdxPVFGCNArRgwknp7D869E2byoUNJa

Merkle Root

9f3d407559670216fbe86ecd1b61fb3a15d8bbd1f0f22d0cdf6e4ca43fffa515
Transactions (1)
Coinbase9f3d4075596702…6e4ca43fffa515
1 in β†’ 1 out7.5600 XPM110 B
AdyAdxPV…2byoUNJa
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.

1.902 Γ— 10⁹⁢(97-digit number)
19029233194532976057…16720035776196607999
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
1.902 Γ— 10⁹⁢(97-digit number)
19029233194532976057…16720035776196607999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.902 Γ— 10⁹⁢(97-digit number)
19029233194532976057…16720035776196608001
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
3.805 Γ— 10⁹⁢(97-digit number)
38058466389065952114…33440071552393215999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.805 Γ— 10⁹⁢(97-digit number)
38058466389065952114…33440071552393216001
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
7.611 Γ— 10⁹⁢(97-digit number)
76116932778131904229…66880143104786431999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
7.611 Γ— 10⁹⁢(97-digit number)
76116932778131904229…66880143104786432001
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
1.522 Γ— 10⁹⁷(98-digit number)
15223386555626380845…33760286209572863999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.522 Γ— 10⁹⁷(98-digit number)
15223386555626380845…33760286209572864001
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
3.044 Γ— 10⁹⁷(98-digit number)
30446773111252761691…67520572419145727999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.044 Γ— 10⁹⁷(98-digit number)
30446773111252761691…67520572419145728001
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
6.089 Γ— 10⁹⁷(98-digit number)
60893546222505523383…35041144838291455999
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:57,963,301 XPMΒ·at block #6,839,874 Β· updates every 60s
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