Block #1,236,476

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 9/14/2015, 2:04:41 PM · Difficulty 10.7550 · 5,575,835 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f37a8128e8d459ae0b975927cb8a84bb6bd02909faf62a42a2da88cd20d888f9

View on Chainz ↗

Height

#1,236,476

Difficulty

10.754998

Transactions

Size

866 B

Version

Bits

0ac1478e

Nonce

1,226,237,673

Timestamp

9/14/2015, 2:04:41 PM

Confirmations

5,575,835

Mined by

⛏️ P2SHAf5GbnXG9kMkLraygoS1sQYPDqAp3rgnDL

Merkle Root

d3098d330e6e57247dbeadb7e690ff690dc7a1eb5bc4f42471421b263c19a98a

Transactions (2)

Coinbase2c668e470f119a…adc20f1bcd426f

1 in → 1 out8.6400 XPM109 B

Af5GbnXG…Ap3rgnDL

58a9bcc0cddff6…38689a474e8610

1 in → 15 out262.4200 XPM667 B

AHwXyvwc…svNS1h8s AeCBsbRG…x61Ldj5e AMuNAQx1…1F2pRV2X AahNe9Eb…j7WvUkU7 AGdCDPCJ…wvuFRxN7

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.

2.931 × 10⁹⁵(96-digit number)

29318758014456621737…61027202824952852159

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

2.931 × 10⁹⁵(96-digit number)

29318758014456621737…61027202824952852159

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.931 × 10⁹⁵(96-digit number)

29318758014456621737…61027202824952852161

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

5.863 × 10⁹⁵(96-digit number)

58637516028913243475…22054405649905704319

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.863 × 10⁹⁵(96-digit number)

58637516028913243475…22054405649905704321

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

1.172 × 10⁹⁶(97-digit number)

11727503205782648695…44108811299811408639

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.172 × 10⁹⁶(97-digit number)

11727503205782648695…44108811299811408641

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

2.345 × 10⁹⁶(97-digit number)

23455006411565297390…88217622599622817279

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.345 × 10⁹⁶(97-digit number)

23455006411565297390…88217622599622817281

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

4.691 × 10⁹⁶(97-digit number)

46910012823130594780…76435245199245634559

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.691 × 10⁹⁶(97-digit number)

46910012823130594780…76435245199245634561

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 #1,236,476

Cookie Preferences