Block #1,179,229

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 8/1/2015, 8:32:45 AM · Difficulty 10.9310 · 5,625,557 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

265b8611b6060674414a67634fc1d559a4a1b1c979c236bdcacff70bad35e15c

View on Chainz ↗

Height

#1,179,229

Difficulty

10.931016

Transactions

Size

14.00 KB

Version

Bits

0aee5714

Nonce

912,555,329

Timestamp

8/1/2015, 8:32:45 AM

Confirmations

5,625,557

Mined by

⛏️ P2SHAcDken9usbU4CW1wAihwrDkHAfhA8Sz5R8

Merkle Root

0611d80c3dcee086fc3268a052037b9ee040dd16bfa890052d4eb54780c2fe7c

Transactions (4)

Coinbasebaac79e55a4fca…6178770df6b2d1

1 in → 1 out8.5200 XPM110 B

AcDken9u…hA8Sz5R8

75411365ac1c55…e84220b6781d78

82 in → 2 out25.1060 XPM11.92 KB

AWQY55hq…va1Q6Gei Aej4QUCz…SVr9QNE3

b2a3c2f6424865…fdbf6e498c64ba

7 in → 2 out60.3363 XPM1.09 KB

AQrNdLqT…N4CyeYjA AQHE5e6H…xDwU3vYU

e222b4a96c7411…d796f16dc8aa02

5 in → 2 out59.7878 XPM819 B

AJjo7qXV…oTb4dcbQ AQHE5e6H…xDwU3vYU

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.

3.924 × 10⁹⁴(95-digit number)

39243093201732285519…81505764967989402999

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

3.924 × 10⁹⁴(95-digit number)

39243093201732285519…81505764967989402999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.924 × 10⁹⁴(95-digit number)

39243093201732285519…81505764967989403001

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

7.848 × 10⁹⁴(95-digit number)

78486186403464571038…63011529935978805999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.848 × 10⁹⁴(95-digit number)

78486186403464571038…63011529935978806001

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

1.569 × 10⁹⁵(96-digit number)

15697237280692914207…26023059871957611999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.569 × 10⁹⁵(96-digit number)

15697237280692914207…26023059871957612001

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

3.139 × 10⁹⁵(96-digit number)

31394474561385828415…52046119743915223999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.139 × 10⁹⁵(96-digit number)

31394474561385828415…52046119743915224001

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

6.278 × 10⁹⁵(96-digit number)

62788949122771656830…04092239487830447999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.278 × 10⁹⁵(96-digit number)

62788949122771656830…04092239487830448001

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