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Block #2,152,058

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 6/8/2017, 7:05:08 PM Β· Difficulty 10.9009 Β· 4,693,145 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
6b0511e05efec8c1ad68194eb58a73ef45af3994281002bfc19eaf7853d3877d
View on Chainz β†—

Height

#2,152,058

Difficulty

10.900901

Transactions

1

Size

198 B

Version

2

Bits

0ae6a16e

Nonce

1,330,264,413

Timestamp

6/8/2017, 7:05:08 PM

Confirmations

4,693,145

Mined by

⛏️ P2SHAS76egxYYCu2cP2u4B9DrFCjuKSDqaTCah

Merkle Root

17aa3b2d24991ec5cba232cede0608d09d9ab38388422233e5167c4eabbaa5dd
Transactions (1)
Coinbase17aa3b2d24991e…167c4eabbaa5dd
1 in β†’ 1 out8.4000 XPM109 B
AS76egxY…SDqaTCah
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.

4.346 Γ— 10⁹²(93-digit number)
43460010148438427361…81867398401786127839
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
4.346 Γ— 10⁹²(93-digit number)
43460010148438427361…81867398401786127839
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.346 Γ— 10⁹²(93-digit number)
43460010148438427361…81867398401786127841
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
8.692 Γ— 10⁹²(93-digit number)
86920020296876854722…63734796803572255679
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
8.692 Γ— 10⁹²(93-digit number)
86920020296876854722…63734796803572255681
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
1.738 Γ— 10⁹³(94-digit number)
17384004059375370944…27469593607144511359
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.738 Γ— 10⁹³(94-digit number)
17384004059375370944…27469593607144511361
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
3.476 Γ— 10⁹³(94-digit number)
34768008118750741888…54939187214289022719
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.476 Γ— 10⁹³(94-digit number)
34768008118750741888…54939187214289022721
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
6.953 Γ— 10⁹³(94-digit number)
69536016237501483777…09878374428578045439
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
6.953 Γ— 10⁹³(94-digit number)
69536016237501483777…09878374428578045441
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:58,006,057 XPMΒ·at block #6,845,202 Β· updates every 60s
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