Block #436,629

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/9/2014, 5:36:43 PM · Difficulty 10.3601 · 6,362,691 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2df63bf823d472c4931dd067b529ae3831f794e38e0d96645f603b3ddb084d8a

View on Chainz ↗

Height

#436,629

Difficulty

10.360090

Transactions

Size

979 B

Version

Bits

0a5c2edd

Nonce

81,832

Timestamp

3/9/2014, 5:36:43 PM

Confirmations

6,362,691

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

78e19c0760d7fd3e97a5e5860bbdd23fd76588d94e9d93d7e191966a8868f777

Transactions (2)

Coinbasee0cddfdc2da8e3…e134e76e0944b9

1 in → 1 out9.3100 XPM116 B

AbwWkWZt…kawDhufa

572a381b5e7865…b6b5219b64a7e8

4 in → 7 out18.9278 XPM773 B

AVE94w5J…WN4TXnY3 AM4zUqtZ…qoQ34B2Y AJvKq8HD…WqkH2BmK Acd9QzkX…HerMkUNx AXHFnvkB…yXdZX2Fh

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.

2.334 × 10⁹⁴(95-digit number)

23346056229396945139…96637803991889852959

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

2.334 × 10⁹⁴(95-digit number)

23346056229396945139…96637803991889852959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.334 × 10⁹⁴(95-digit number)

23346056229396945139…96637803991889852961

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

4.669 × 10⁹⁴(95-digit number)

46692112458793890278…93275607983779705919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.669 × 10⁹⁴(95-digit number)

46692112458793890278…93275607983779705921

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

9.338 × 10⁹⁴(95-digit number)

93384224917587780557…86551215967559411839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.338 × 10⁹⁴(95-digit number)

93384224917587780557…86551215967559411841

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

1.867 × 10⁹⁵(96-digit number)

18676844983517556111…73102431935118823679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.867 × 10⁹⁵(96-digit number)

18676844983517556111…73102431935118823681

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

3.735 × 10⁹⁵(96-digit number)

37353689967035112222…46204863870237647359

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.735 × 10⁹⁵(96-digit number)

37353689967035112222…46204863870237647361

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