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Block #2,650,362

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/5/2018, 11:56:34 PM Β· Difficulty 11.7571 Β· 4,190,716 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
4aa27c13abfd1a77b00799c0d3c2c9184c6e77389966d91bdffd769f425049d8
View on Chainz β†—

Height

#2,650,362

Difficulty

11.757123

Transactions

1

Size

200 B

Version

2

Bits

0bc1d2d3

Nonce

498,080,156

Timestamp

5/5/2018, 11:56:34 PM

Confirmations

4,190,716

Mined by

⛏️ P2SHAdqah8zh3AxeLUnA13CQCRpLQc1WwoHJ9t

Merkle Root

8687a604e4b0561c1486aa8390179495b6edb9060ea331f06171dd575f61321f
Transactions (1)
Coinbase8687a604e4b056…71dd575f61321f
1 in β†’ 1 out7.2200 XPM110 B
Adqah8zh…1WwoHJ9t
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.

5.175 Γ— 10⁹³(94-digit number)
51754399913656433790…07591190984864609279
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
5.175 Γ— 10⁹³(94-digit number)
51754399913656433790…07591190984864609279
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.175 Γ— 10⁹³(94-digit number)
51754399913656433790…07591190984864609281
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
1.035 Γ— 10⁹⁴(95-digit number)
10350879982731286758…15182381969729218559
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.035 Γ— 10⁹⁴(95-digit number)
10350879982731286758…15182381969729218561
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
2.070 Γ— 10⁹⁴(95-digit number)
20701759965462573516…30364763939458437119
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.070 Γ— 10⁹⁴(95-digit number)
20701759965462573516…30364763939458437121
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
4.140 Γ— 10⁹⁴(95-digit number)
41403519930925147032…60729527878916874239
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.140 Γ— 10⁹⁴(95-digit number)
41403519930925147032…60729527878916874241
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
8.280 Γ— 10⁹⁴(95-digit number)
82807039861850294065…21459055757833748479
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
8.280 Γ— 10⁹⁴(95-digit number)
82807039861850294065…21459055757833748481
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
1.656 Γ— 10⁹⁡(96-digit number)
16561407972370058813…42918111515667496959
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:57,972,986 XPMΒ·at block #6,841,077 Β· updates every 60s
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