Block #1,356,479

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/5/2015, 10:07:13 PM · Difficulty 10.8202 · 5,450,210 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

23eff14ad3c2a1047715e53ec60317aa7ea17a96cb4a2e72a5941bcf87ef6e7b

View on Chainz ↗

Height

#1,356,479

Difficulty

10.820171

Transactions

Size

1.13 KB

Version

Bits

0ad1f6be

Nonce

324,388,433

Timestamp

12/5/2015, 10:07:13 PM

Confirmations

5,450,210

Mined by

⛏️ P2SHAP7t4zyjGHXRd2PRERZQXKJSvghcoGVEcj

Merkle Root

dc845409a3994758124b59cccf0152e5940bd49d120377bab66583800571a7cd

Transactions (3)

Coinbase6ed2525f308623…c6865efd310cfb

1 in → 1 out8.5500 XPM109 B

AP7t4zyj…hcoGVEcj

3cc2346c0cd867…802028b9fc1d27

1 in → 17 out35.2534 XPM735 B

ALf6Qgbz…ToZEpAEr AJKTpQgz…FPxCAbYA AGGC96kT…tgntK4X9 AMzr3hAG…ECsZkWDx ANgDtM3s…sh2FT6eP

29618ddb2a2f52…19cb7e87b799c4

1 in → 2 out6.1262 XPM225 B

ASoTAh16…34qrQ5sU AcuM7XiJ…5uND8Jce

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.

3.994 × 10⁹⁵(96-digit number)

39945329067435155854…88161169166944459519

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

3.994 × 10⁹⁵(96-digit number)

39945329067435155854…88161169166944459519

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.994 × 10⁹⁵(96-digit number)

39945329067435155854…88161169166944459521

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

7.989 × 10⁹⁵(96-digit number)

79890658134870311708…76322338333888919039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.989 × 10⁹⁵(96-digit number)

79890658134870311708…76322338333888919041

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

1.597 × 10⁹⁶(97-digit number)

15978131626974062341…52644676667777838079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.597 × 10⁹⁶(97-digit number)

15978131626974062341…52644676667777838081

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

3.195 × 10⁹⁶(97-digit number)

31956263253948124683…05289353335555676159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.195 × 10⁹⁶(97-digit number)

31956263253948124683…05289353335555676161

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

6.391 × 10⁹⁶(97-digit number)

63912526507896249367…10578706671111352319

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.391 × 10⁹⁶(97-digit number)

63912526507896249367…10578706671111352321

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 #1,356,479

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