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Block #1,434,838

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 1/29/2016, 2:06:22 PM Β· Difficulty 10.8096 Β· 5,404,371 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
e28e4f7e9f754fcf2c1cd44a035a9d02516e3e45ed6973f5be5babd19f3c21e2
View on Chainz β†—

Height

#1,434,838

Difficulty

10.809587

Transactions

2

Size

5.76 KB

Version

2

Bits

0acf4118

Nonce

115,351,854

Timestamp

1/29/2016, 2:06:22 PM

Confirmations

5,404,371

Mined by

⛏️ P2SHASCoemZsgjnXA6yK1WZdJn5pL82aJLKfBb

Merkle Root

34de9a8b4c480f10965c8b764642597c263163acfef3b9209dbb8d6fb379ba51
Transactions (2)
Coinbase98a37f0472e13a…7213c74831bb7b
1 in β†’ 1 out8.6000 XPM110 B
ASCoemZs…2aJLKfBb
e62b3b059b53b4…6baeea8c46e2f8
38 in β†’ 2 out719.6000 XPM5.56 KB
AcDhjHA9…ebukETHzAUbDM1iL…R4hX1ahB
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.

6.380 Γ— 10⁹⁷(98-digit number)
63803551032419534663…21509969004589629439
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
6.380 Γ— 10⁹⁷(98-digit number)
63803551032419534663…21509969004589629439
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
6.380 Γ— 10⁹⁷(98-digit number)
63803551032419534663…21509969004589629441
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
1.276 Γ— 10⁹⁸(99-digit number)
12760710206483906932…43019938009179258879
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.276 Γ— 10⁹⁸(99-digit number)
12760710206483906932…43019938009179258881
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
2.552 Γ— 10⁹⁸(99-digit number)
25521420412967813865…86039876018358517759
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.552 Γ— 10⁹⁸(99-digit number)
25521420412967813865…86039876018358517761
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
5.104 Γ— 10⁹⁸(99-digit number)
51042840825935627730…72079752036717035519
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.104 Γ— 10⁹⁸(99-digit number)
51042840825935627730…72079752036717035521
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
1.020 Γ— 10⁹⁹(100-digit number)
10208568165187125546…44159504073434071039
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.020 Γ— 10⁹⁹(100-digit number)
10208568165187125546…44159504073434071041
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,957,953 XPMΒ·at block #6,839,208 Β· updates every 60s
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