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Block #934,290

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 2/13/2015, 6:10:17 AM Β· Difficulty 10.9017 Β· 5,876,566 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
ffe4d0303b9c71ddd4ea8c673a608ff8165f059b26d9fa50b662813e61a1dbe7
View on Chainz β†—

Height

#934,290

Difficulty

10.901740

Transactions

2

Size

7.50 KB

Version

2

Bits

0ae6d869

Nonce

1,092,301,749

Timestamp

2/13/2015, 6:10:17 AM

Confirmations

5,876,566

Mined by

⛏️ P2SHAUsNKur8s2Yr1nYuWPjiGUaujW63uw9oRn

Merkle Root

fd1b095d592aaa955ca93f810c28ce6c91759152156df65a6a47f8c8f869833b
Transactions (2)
Coinbase0a8470f2079d98…61315fcf67d36f
1 in β†’ 1 out8.4800 XPM109 B
AUsNKur8…63uw9oRn
aed33d7f037b6e…ae42ac4eb39604
50 in β†’ 2 out500.0255 XPM7.30 KB
AJjnK9uC…VreFquR4AWJufLUo…gYnPxFd1
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.

7.175 Γ— 10⁹⁴(95-digit number)
71754709874204164407…60050169230902879999
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
7.175 Γ— 10⁹⁴(95-digit number)
71754709874204164407…60050169230902879999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
7.175 Γ— 10⁹⁴(95-digit number)
71754709874204164407…60050169230902880001
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
1.435 Γ— 10⁹⁡(96-digit number)
14350941974840832881…20100338461805759999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.435 Γ— 10⁹⁡(96-digit number)
14350941974840832881…20100338461805760001
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
2.870 Γ— 10⁹⁡(96-digit number)
28701883949681665762…40200676923611519999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.870 Γ— 10⁹⁡(96-digit number)
28701883949681665762…40200676923611520001
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
5.740 Γ— 10⁹⁡(96-digit number)
57403767899363331525…80401353847223039999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.740 Γ— 10⁹⁡(96-digit number)
57403767899363331525…80401353847223040001
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
1.148 Γ— 10⁹⁢(97-digit number)
11480753579872666305…60802707694446079999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.148 Γ— 10⁹⁢(97-digit number)
11480753579872666305…60802707694446080001
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
2.296 Γ— 10⁹⁢(97-digit number)
22961507159745332610…21605415388892159999
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:57,730,943 XPMΒ·at block #6,810,855 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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