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Block #1,534,613

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 4/10/2016, 8:52:50 AM Β· Difficulty 10.6173 Β· 5,281,193 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
29e828c2783761ebf67952b228189f29b20aed176fb7a3ff9959aa3f959408fe
View on Chainz β†—

Height

#1,534,613

Difficulty

10.617350

Transactions

2

Size

7.60 KB

Version

2

Bits

0a9e0aa2

Nonce

240,519,986

Timestamp

4/10/2016, 8:52:50 AM

Confirmations

5,281,193

Mined by

⛏️ P2SHAQ4VkGSmbpYC5HoPMcK3Hz8idLcXDciYGr

Merkle Root

f5f80ed985c79eb29420d5566e01d43cf4fb10a06f252fc9a90286db4de792e4
Transactions (2)
Coinbase0821a9fa1a46a0…d91c8ddae524da
1 in β†’ 1 out8.9400 XPM110 B
AQ4VkGSm…cXDciYGr
84377a371ca1ec…128853b0a1b1a2
51 in β†’ 1 out2960.9360 XPM7.41 KB
ARF5wKyD…vCjnps2J
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.

1.691 Γ— 10⁹⁴(95-digit number)
16910349092479956894…35259094843955976959
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
1.691 Γ— 10⁹⁴(95-digit number)
16910349092479956894…35259094843955976959
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.691 Γ— 10⁹⁴(95-digit number)
16910349092479956894…35259094843955976961
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
3.382 Γ— 10⁹⁴(95-digit number)
33820698184959913788…70518189687911953919
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.382 Γ— 10⁹⁴(95-digit number)
33820698184959913788…70518189687911953921
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
6.764 Γ— 10⁹⁴(95-digit number)
67641396369919827576…41036379375823907839
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.764 Γ— 10⁹⁴(95-digit number)
67641396369919827576…41036379375823907841
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
1.352 Γ— 10⁹⁡(96-digit number)
13528279273983965515…82072758751647815679
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.352 Γ— 10⁹⁡(96-digit number)
13528279273983965515…82072758751647815681
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
2.705 Γ— 10⁹⁡(96-digit number)
27056558547967931030…64145517503295631359
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.705 Γ— 10⁹⁡(96-digit number)
27056558547967931030…64145517503295631361
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:57,770,554 XPMΒ·at block #6,815,805 Β· updates every 60s
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