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Block #2,793,446

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 8/14/2018, 10:06:07 AM Β· Difficulty 11.6760 Β· 4,048,768 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
eafbc643a36d7789541d714d780de2d07c15bf8c3b0a042354bc30cee666bc7b
View on Chainz β†—

Height

#2,793,446

Difficulty

11.676009

Transactions

1

Size

200 B

Version

2

Bits

0bad0eef

Nonce

1,565,926,551

Timestamp

8/14/2018, 10:06:07 AM

Confirmations

4,048,768

Mined by

⛏️ P2SHALhRrgdHiNGQ8yTvsvR5E5nuWMkyMbNP2B

Merkle Root

898e6fc6d023ab0f3f558f16bb255fd813d786259de72b2f81ab4e97d753956c
Transactions (1)
Coinbase898e6fc6d023ab…ab4e97d753956c
1 in β†’ 1 out7.3200 XPM110 B
ALhRrgdH…kyMbNP2B
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.

9.489 Γ— 10⁹³(94-digit number)
94890784140418412489…46145077573767133439
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
9.489 Γ— 10⁹³(94-digit number)
94890784140418412489…46145077573767133439
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
9.489 Γ— 10⁹³(94-digit number)
94890784140418412489…46145077573767133441
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
1.897 Γ— 10⁹⁴(95-digit number)
18978156828083682497…92290155147534266879
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.897 Γ— 10⁹⁴(95-digit number)
18978156828083682497…92290155147534266881
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
3.795 Γ— 10⁹⁴(95-digit number)
37956313656167364995…84580310295068533759
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.795 Γ— 10⁹⁴(95-digit number)
37956313656167364995…84580310295068533761
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
7.591 Γ— 10⁹⁴(95-digit number)
75912627312334729991…69160620590137067519
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
7.591 Γ— 10⁹⁴(95-digit number)
75912627312334729991…69160620590137067521
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
1.518 Γ— 10⁹⁡(96-digit number)
15182525462466945998…38321241180274135039
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.518 Γ— 10⁹⁡(96-digit number)
15182525462466945998…38321241180274135041
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
3.036 Γ— 10⁹⁡(96-digit number)
30365050924933891996…76642482360548270079
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:57,982,109 XPMΒ·at block #6,842,213 Β· updates every 60s
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