Block #856,547

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 12/17/2014, 3:54:46 AM · Difficulty 10.9681 · 5,948,541 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

104793483c8500fa3e87ce8526800d2e9b48b6bca231485474299332c81ec3a5

View on Chainz ↗

Height

#856,547

Difficulty

10.968089

Transactions

Size

3.25 KB

Version

Bits

0af7d4ab

Nonce

1,932,316,010

Timestamp

12/17/2014, 3:54:46 AM

Confirmations

5,948,541

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

e0028b9609308c33d90b6396df3603cf71ff56c36a964537d322d6d2cd271946

Transactions (3)

Coinbaseb7305d6b641df1…5c066ddb670718

1 in → 1 out8.3550 XPM116 B

ANSXnLY2…Sd25TjkD

ab1aba422e4e3a…f646bb8bb33b7a

19 in → 2 out12.9422 XPM2.82 KB

AHjev3cX…MpNoCtuM AJdM6BQD…g1g59wty

ce0b92dfbe52fb…b53d2899a7f0d7

1 in → 2 out0.0646 XPM226 B

AXcxnfQ7…d18YA9Wv AG1zVuXr…xB5KV97g

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.

1.533 × 10⁹⁸(99-digit number)

15332563041215224756…96362933623161405439

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

1.533 × 10⁹⁸(99-digit number)

15332563041215224756…96362933623161405439

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.533 × 10⁹⁸(99-digit number)

15332563041215224756…96362933623161405441

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

3.066 × 10⁹⁸(99-digit number)

30665126082430449513…92725867246322810879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.066 × 10⁹⁸(99-digit number)

30665126082430449513…92725867246322810881

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

6.133 × 10⁹⁸(99-digit number)

61330252164860899026…85451734492645621759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.133 × 10⁹⁸(99-digit number)

61330252164860899026…85451734492645621761

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

1.226 × 10⁹⁹(100-digit number)

12266050432972179805…70903468985291243519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.226 × 10⁹⁹(100-digit number)

12266050432972179805…70903468985291243521

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

2.453 × 10⁹⁹(100-digit number)

24532100865944359610…41806937970582487039

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.453 × 10⁹⁹(100-digit number)

24532100865944359610…41806937970582487041

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

4.906 × 10⁹⁹(100-digit number)

49064201731888719221…83613875941164974079

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