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Block #2,847,260

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 9/20/2018, 3:17:15 AM Β· Difficulty 11.7329 Β· 3,992,131 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
89c7aec0fbbf9167ebc13420d9b55db21dbe7833df3fc4cdb5ace8bfb4d6c944
View on Chainz β†—

Height

#2,847,260

Difficulty

11.732904

Transactions

1

Size

200 B

Version

2

Bits

0bbb9f93

Nonce

1,208,830,333

Timestamp

9/20/2018, 3:17:15 AM

Confirmations

3,992,131

Mined by

⛏️ P2SHAbGkMksHbi5cxbakvrGYKibH6T6SETuvJm

Merkle Root

73cc72c244475104249a0a8987e964eeccc469af44c4480573ef818073f13655
Transactions (1)
Coinbase73cc72c2444751…ef818073f13655
1 in β†’ 1 out7.2500 XPM110 B
AbGkMksH…6SETuvJm
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.

8.770 Γ— 10⁹⁴(95-digit number)
87709098710488335673…54676895235967414559
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
8.770 Γ— 10⁹⁴(95-digit number)
87709098710488335673…54676895235967414559
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
8.770 Γ— 10⁹⁴(95-digit number)
87709098710488335673…54676895235967414561
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
1.754 Γ— 10⁹⁡(96-digit number)
17541819742097667134…09353790471934829119
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.754 Γ— 10⁹⁡(96-digit number)
17541819742097667134…09353790471934829121
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
3.508 Γ— 10⁹⁡(96-digit number)
35083639484195334269…18707580943869658239
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.508 Γ— 10⁹⁡(96-digit number)
35083639484195334269…18707580943869658241
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
7.016 Γ— 10⁹⁡(96-digit number)
70167278968390668538…37415161887739316479
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
7.016 Γ— 10⁹⁡(96-digit number)
70167278968390668538…37415161887739316481
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
1.403 Γ— 10⁹⁢(97-digit number)
14033455793678133707…74830323775478632959
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.403 Γ— 10⁹⁢(97-digit number)
14033455793678133707…74830323775478632961
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
2.806 Γ— 10⁹⁢(97-digit number)
28066911587356267415…49660647550957265919
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:57,959,412 XPMΒ·at block #6,839,390 Β· updates every 60s
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