Block #235,621

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/31/2013, 1:05:10 AM · Difficulty 9.9458 · 6,574,561 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b913495d74cf397acf770f51d801527e809d16f6278ab4084fc313945ee37d8b

View on Chainz ↗

Height

#235,621

Difficulty

9.945850

Transactions

Size

1.11 KB

Version

Bits

09f22332

Nonce

29,792

Timestamp

10/31/2013, 1:05:10 AM

Confirmations

6,574,561

Mined by

⛏️ P2SHAZDUEbdSvp8cw8AAZ1fERZUqSYRYKMRZET

Merkle Root

5a789bca8085b7a84d7fed7747fcbe40f77a9ddb29f1e3e8d5541e083250fd99

Transactions (4)

Coinbase6e74b85990bb08…c5c2e25deb341d

1 in → 2 out10.1200 XPM137 B

AZDUEbdS…RYKMRZET ASNt3cJa…L5zCqAYM

b90c1526080976…38fff86f233195

1 in → 1 out10.1200 XPM158 B

AdRhBEEu…68A4jiit

5b2969442237a9…bd19d65fbb84c0

2 in → 2 out10.6281 XPM374 B

AVTAF4Wj…GfDJJ3sr ASuoUi24…FwBoFbxd

da9ef51e63f6e3…e31ef024a56130

2 in → 2 out2.4473 XPM373 B

ATk6ixZb…zK667i9H AXV3ABaL…uFUj41VU

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.

4.024 × 10⁹⁷(98-digit number)

40244580416873213544…29764324946223902199

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

4.024 × 10⁹⁷(98-digit number)

40244580416873213544…29764324946223902199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.024 × 10⁹⁷(98-digit number)

40244580416873213544…29764324946223902201

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

8.048 × 10⁹⁷(98-digit number)

80489160833746427089…59528649892447804399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.048 × 10⁹⁷(98-digit number)

80489160833746427089…59528649892447804401

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

1.609 × 10⁹⁸(99-digit number)

16097832166749285417…19057299784895608799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.609 × 10⁹⁸(99-digit number)

16097832166749285417…19057299784895608801

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

3.219 × 10⁹⁸(99-digit number)

32195664333498570835…38114599569791217599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.219 × 10⁹⁸(99-digit number)

32195664333498570835…38114599569791217601

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

6.439 × 10⁹⁸(99-digit number)

64391328666997141671…76229199139582435199

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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 #235,621

Cookie Preferences