Block #969,650

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/11/2015, 5:35:39 PM · Difficulty 10.8324 · 5,837,188 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3bdf6f94cb575f1e6b18ef744b831fc257ed5bb848cffb003b4b7f0856e87561

View on Chainz ↗

Height

#969,650

Difficulty

10.832372

Transactions

Size

5.41 KB

Version

Bits

0ad5165d

Nonce

255,300,773

Timestamp

3/11/2015, 5:35:39 PM

Confirmations

5,837,188

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

bd4a595172a47ea36d4b62403ce8a407a983148312c83feffed1eacd0f9f69d8

Transactions (4)

Coinbasefc89f2b65eeb71…d490babaab48e5

1 in → 1 out8.5700 XPM116 B

ANSXnLY2…Sd25TjkD

533afdfe469e95…bafa31ac2e6320

1 in → 41 out16.9700 XPM1.52 KB

AHqfaYRY…QeWTKjso AYR35hRG…hekAp2hn ANACbdDE…vs7hJHst AZcVpcEA…UtbpTRFR AXLkjH6Q…9wXKhR9V

1ef8c44f1fe146…27ecbfb5c3ac6d

1 in → 51 out13.1480 XPM1.85 KB

ALNpqWV2…CFZwxaAK AS8tXSFT…PVqdRMGe ARbmELZZ…D2EmA9eK AehrqrWL…agQE4q4U ATVsibFx…d9DzXD1L

f30e029f769198…fcc7ca03f83e87

1 in → 51 out3.8812 XPM1.85 KB

AJab5pQJ…NDncq51r ALqDX1bt…BRvuXQjZ AJXX5a9u…FC7p5XjF AcKQReo9…sTqY6wG6 AZmQ1g4i…Jv7H627y

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.

2.435 × 10⁹⁶(97-digit number)

24352992572819060915…75743635723364228159

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

2.435 × 10⁹⁶(97-digit number)

24352992572819060915…75743635723364228159

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.435 × 10⁹⁶(97-digit number)

24352992572819060915…75743635723364228161

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

4.870 × 10⁹⁶(97-digit number)

48705985145638121831…51487271446728456319

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.870 × 10⁹⁶(97-digit number)

48705985145638121831…51487271446728456321

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

9.741 × 10⁹⁶(97-digit number)

97411970291276243662…02974542893456912639

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.741 × 10⁹⁶(97-digit number)

97411970291276243662…02974542893456912641

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

1.948 × 10⁹⁷(98-digit number)

19482394058255248732…05949085786913825279

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.948 × 10⁹⁷(98-digit number)

19482394058255248732…05949085786913825281

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

3.896 × 10⁹⁷(98-digit number)

38964788116510497465…11898171573827650559

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.896 × 10⁹⁷(98-digit number)

38964788116510497465…11898171573827650561

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

Block #969,650

Cookie Preferences