Block #918,172

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/1/2015, 5:15:34 AM · Difficulty 10.9223 · 5,878,171 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

60b6be3d207b23b536e69484696c088e94433dee6c51de783188c76ae560af63

View on Chainz ↗

Height

#918,172

Difficulty

10.922348

Transactions

Size

1017 B

Version

Bits

0aec1efb

Nonce

115,275,900

Timestamp

2/1/2015, 5:15:34 AM

Confirmations

5,878,171

Mined by

⛏️ P2SHAcVuxZ4zyEKE8a54YQSDC3eAuLpQARPzkJ

Merkle Root

60b993f400425647db61c09cea2e56a4dab0e24b36e112f6f574e98407ed8e7a

Transactions (2)

Coinbase82b3f5900e3e4d…ab4d92fe1ca8f6

1 in → 1 out8.3900 XPM109 B

AcVuxZ4z…pQARPzkJ

db2c8bca1d7960…8d3cd858443159

5 in → 2 out1278.3807 XPM817 B

AQhw1bo8…U9xpwjus ALrbGZqy…tzbLmEFU

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.

4.576 × 10⁹⁷(98-digit number)

45765187809180187044…74045348428052766719

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

4.576 × 10⁹⁷(98-digit number)

45765187809180187044…74045348428052766719

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.576 × 10⁹⁷(98-digit number)

45765187809180187044…74045348428052766721

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

9.153 × 10⁹⁷(98-digit number)

91530375618360374088…48090696856105533439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.153 × 10⁹⁷(98-digit number)

91530375618360374088…48090696856105533441

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

1.830 × 10⁹⁸(99-digit number)

18306075123672074817…96181393712211066879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.830 × 10⁹⁸(99-digit number)

18306075123672074817…96181393712211066881

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

3.661 × 10⁹⁸(99-digit number)

36612150247344149635…92362787424422133759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.661 × 10⁹⁸(99-digit number)

36612150247344149635…92362787424422133761

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

7.322 × 10⁹⁸(99-digit number)

73224300494688299270…84725574848844267519

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.322 × 10⁹⁸(99-digit number)

73224300494688299270…84725574848844267521

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