Block #912,449

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/27/2015, 10:15:22 PM · Difficulty 10.9289 · 5,880,316 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8f4689bd8a96f010aafa9943467d236739c4d7e01418d955b7051de75e5f02f0

View on Chainz ↗

Height

#912,449

Difficulty

10.928911

Transactions

Size

1.15 KB

Version

Bits

0aedcd21

Nonce

707,677,400

Timestamp

1/27/2015, 10:15:22 PM

Confirmations

5,880,316

Merkle Root

3773f49fcc6f4f94b556c49e43c05ddb2c6e6f8d513290175c1b8250830cfcd6

Transactions (2)

Coinbase9c005a37386162…718ba873aae272

1 in → 1 out8.4300 XPM116 B

ANSXnLY2…Sd25TjkD

a016835c708a53…d64510c4bebff0

6 in → 2 out3305.7851 XPM969 B

AV1pFcbm…bDQEzNHk AUSxVrre…B27XD3yv

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.

2.826 × 10⁹⁸(99-digit number)

28261677711415854808…38517842111670271999

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

2.826 × 10⁹⁸(99-digit number)

28261677711415854808…38517842111670271999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.826 × 10⁹⁸(99-digit number)

28261677711415854808…38517842111670272001

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

5.652 × 10⁹⁸(99-digit number)

56523355422831709616…77035684223340543999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.652 × 10⁹⁸(99-digit number)

56523355422831709616…77035684223340544001

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

1.130 × 10⁹⁹(100-digit number)

11304671084566341923…54071368446681087999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.130 × 10⁹⁹(100-digit number)

11304671084566341923…54071368446681088001

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

2.260 × 10⁹⁹(100-digit number)

22609342169132683846…08142736893362175999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.260 × 10⁹⁹(100-digit number)

22609342169132683846…08142736893362176001

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

4.521 × 10⁹⁹(100-digit number)

45218684338265367693…16285473786724351999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.521 × 10⁹⁹(100-digit number)

45218684338265367693…16285473786724352001

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