Block #2,273,149

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 8/29/2017, 9:42:15 AM · Difficulty 10.9543 · 4,560,777 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a1c1f82856aa40ecea1b7ea376574a18c4e5842440d87f9eee07a93fb4ad0334

View on Chainz ↗

Height

#2,273,149

Difficulty

10.954261

Transactions

Size

1014 B

Version

Bits

0af44a73

Nonce

525,833,870

Timestamp

8/29/2017, 9:42:15 AM

Confirmations

4,560,777

Mined by

⛏️ P2SHANjVdMPeBwgGoQpvXkAATKe6NDWLQfegXt

Merkle Root

49720d8a4f26485416b8ff953bccc5550763f0bf891436ea65a6817be9bf3fd1

Transactions (2)

Coinbase9a4f1cfafd851e…4dea12f634845f

1 in → 1 out8.3300 XPM109 B

ANjVdMPe…WLQfegXt

bd0663de9b2f97…8413a211a70227

5 in → 2 out32.0200 XPM815 B

AU5bsQFi…RA19fWTB AbZk7SNL…KemG3ko6

Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) — it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

2.077 × 10⁹⁵(96-digit number)

20771340938344533449…85956274699454656639

Discovered Prime Numbers

Lower: 2^k × origin − 1 | Upper: 2^k × 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 — Twin Prime Pair (origin ± 1)

origin − 1

2.077 × 10⁹⁵(96-digit number)

20771340938344533449…85956274699454656639

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.077 × 10⁹⁵(96-digit number)

20771340938344533449…85956274699454656641

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: origin + 1 − origin − 1 = 2 (twin primes ✓)

Level 1 — Twin Prime Pair (2^1 × origin ± 1)

2^1 × origin − 1

4.154 × 10⁹⁵(96-digit number)

41542681876689066898…71912549398909313279

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.154 × 10⁹⁵(96-digit number)

41542681876689066898…71912549398909313281

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^1 × origin + 1 − 2^1 × origin − 1 = 2 (twin primes ✓)

Level 2 — Twin Prime Pair (2^2 × origin ± 1)

2^2 × origin − 1

8.308 × 10⁹⁵(96-digit number)

83085363753378133797…43825098797818626559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.308 × 10⁹⁵(96-digit number)

83085363753378133797…43825098797818626561

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^2 × origin + 1 − 2^2 × origin − 1 = 2 (twin primes ✓)

Level 3 — Twin Prime Pair (2^3 × origin ± 1)

2^3 × origin − 1

1.661 × 10⁹⁶(97-digit number)

16617072750675626759…87650197595637253119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.661 × 10⁹⁶(97-digit number)

16617072750675626759…87650197595637253121

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

Level 4 — Twin Prime Pair (2^4 × origin ± 1)

2^4 × origin − 1

3.323 × 10⁹⁶(97-digit number)

33234145501351253518…75300395191274506239

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.323 × 10⁹⁶(97-digit number)

33234145501351253518…75300395191274506241

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 consecutive prime numbers forming a Bi-Twin Chain. The prime chain origin — the large number shown above — anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

★★☆☆☆

Rarity

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)

Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — 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 − 1 and p+2 = origin/primorial + 1

Cross-reference on Chainz Explorer

Block #2,273,149

Cookie Preferences