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Block #2,868,010

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 10/5/2018, 7:35:49 AM Β· Difficulty 11.6680 Β· 3,974,293 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
7d293d5f32e257bbdbe2f20435c61e61ed3282c2814caa61dc49627983f93034
View on Chainz β†—

Height

#2,868,010

Difficulty

11.668011

Transactions

1

Size

201 B

Version

2

Bits

0bab02c2

Nonce

1,314,069,603

Timestamp

10/5/2018, 7:35:49 AM

Confirmations

3,974,293

Mined by

⛏️ P2SHAUMQRepmQQz6L5K9d1Muaf8ABjtAfKmdW1

Merkle Root

78608a2c029cfcc52d7328fdc8fbcfe2d2ac13229232e5f111a4f85abfab38f9
Transactions (1)
Coinbase78608a2c029cfc…a4f85abfab38f9
1 in β†’ 1 out7.3300 XPM110 B
AUMQRepm…tAfKmdW1
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.

1.445 Γ— 10⁹⁢(97-digit number)
14453528508578479887…27891717006200315679
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
1.445 Γ— 10⁹⁢(97-digit number)
14453528508578479887…27891717006200315679
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.445 Γ— 10⁹⁢(97-digit number)
14453528508578479887…27891717006200315681
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
2.890 Γ— 10⁹⁢(97-digit number)
28907057017156959774…55783434012400631359
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.890 Γ— 10⁹⁢(97-digit number)
28907057017156959774…55783434012400631361
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
5.781 Γ— 10⁹⁢(97-digit number)
57814114034313919549…11566868024801262719
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.781 Γ— 10⁹⁢(97-digit number)
57814114034313919549…11566868024801262721
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
1.156 Γ— 10⁹⁷(98-digit number)
11562822806862783909…23133736049602525439
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.156 Γ— 10⁹⁷(98-digit number)
11562822806862783909…23133736049602525441
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
2.312 Γ— 10⁹⁷(98-digit number)
23125645613725567819…46267472099205050879
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.312 Γ— 10⁹⁷(98-digit number)
23125645613725567819…46267472099205050881
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
4.625 Γ— 10⁹⁷(98-digit number)
46251291227451135639…92534944198410101759
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:57,982,829 XPMΒ·at block #6,842,302 Β· updates every 60s
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