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Block #2,280,280

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 9/3/2017, 5:29:56 AM Β· Difficulty 10.9561 Β· 4,550,604 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
46cab7047c372198c8b629d18e39f07ec6253838222c2bd26e87831ada13144c
View on Chainz β†—

Height

#2,280,280

Difficulty

10.956123

Transactions

2

Size

425 B

Version

2

Bits

0af4c478

Nonce

226,243,978

Timestamp

9/3/2017, 5:29:56 AM

Confirmations

4,550,604

Mined by

⛏️ P2SHAWXdS3iPJxeg2P93kUsYcUeeANi7mGjBVx

Merkle Root

9284210f8acf86ffd7010d5733ef636357b15259f537a8386c0f0802a6b2e149
Transactions (2)
Coinbase6c07e680214411…c746c757ee7504
1 in β†’ 1 out8.3300 XPM110 B
AWXdS3iP…i7mGjBVx
cf3603baee4e20…3a3fa1904b402d
1 in β†’ 2 out2486.5759 XPM225 B
AS8Swa5k…emSJQqiEAK9JEpBJ…DByMt7k3
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.

3.587 Γ— 10⁹⁡(96-digit number)
35876721699048394922…48442757573777242879
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
3.587 Γ— 10⁹⁡(96-digit number)
35876721699048394922…48442757573777242879
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.587 Γ— 10⁹⁡(96-digit number)
35876721699048394922…48442757573777242881
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
7.175 Γ— 10⁹⁡(96-digit number)
71753443398096789845…96885515147554485759
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
7.175 Γ— 10⁹⁡(96-digit number)
71753443398096789845…96885515147554485761
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
1.435 Γ— 10⁹⁢(97-digit number)
14350688679619357969…93771030295108971519
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.435 Γ— 10⁹⁢(97-digit number)
14350688679619357969…93771030295108971521
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
2.870 Γ— 10⁹⁢(97-digit number)
28701377359238715938…87542060590217943039
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.870 Γ— 10⁹⁢(97-digit number)
28701377359238715938…87542060590217943041
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
5.740 Γ— 10⁹⁢(97-digit number)
57402754718477431876…75084121180435886079
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.740 Γ— 10⁹⁢(97-digit number)
57402754718477431876…75084121180435886081
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
1.148 Γ— 10⁹⁷(98-digit number)
11480550943695486375…50168242360871772159
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:57,891,208 XPMΒ·at block #6,830,883 Β· updates every 60s
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