Block #785,561

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 10/27/2014, 4:37:55 PM · Difficulty 10.9750 · 6,010,552 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3e4ab8070caf2ba58730ed6cd4ecb1965150184da4062e13672be13db919209d

View on Chainz ↗

Height

#785,561

Difficulty

10.975019

Transactions

Size

775 B

Version

Bits

0af99adb

Nonce

1,326,893,970

Timestamp

10/27/2014, 4:37:55 PM

Confirmations

6,010,552

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

99f4d6ff84b94ac566d9c193398882078bad345d1b833df3441cc6e55714273a

Transactions (3)

Coinbasec03a165bcdff0d…786bb2e6325196

1 in → 1 out8.3100 XPM116 B

ANSXnLY2…Sd25TjkD

ae5bee585be011…d74fbb79a83fa1

2 in → 1 out1.6187 XPM341 B

ASLwqNEo…1ccEZYHV

d68b61d062e7a1…7d0f036573407e

1 in → 2 out6.8047 XPM227 B

AVbVNKtM…UFxAXDDY AecWKeHk…kgB2mTAH

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.

8.624 × 10⁹⁵(96-digit number)

86248979118175833212…52536112982971199999

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

8.624 × 10⁹⁵(96-digit number)

86248979118175833212…52536112982971199999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.624 × 10⁹⁵(96-digit number)

86248979118175833212…52536112982971200001

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

1.724 × 10⁹⁶(97-digit number)

17249795823635166642…05072225965942399999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.724 × 10⁹⁶(97-digit number)

17249795823635166642…05072225965942400001

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

3.449 × 10⁹⁶(97-digit number)

34499591647270333285…10144451931884799999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.449 × 10⁹⁶(97-digit number)

34499591647270333285…10144451931884800001

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

6.899 × 10⁹⁶(97-digit number)

68999183294540666570…20288903863769599999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.899 × 10⁹⁶(97-digit number)

68999183294540666570…20288903863769600001

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

1.379 × 10⁹⁷(98-digit number)

13799836658908133314…40577807727539199999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.379 × 10⁹⁷(98-digit number)

13799836658908133314…40577807727539200001

Verify on FactorDB ↗Wolfram Alpha ↗

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

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

2.759 × 10⁹⁷(98-digit number)

27599673317816266628…81155615455078399999

Verify on FactorDB ↗Wolfram Alpha ↗

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 — 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

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 × 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