Block #459,935

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/25/2014, 3:35:06 PM · Difficulty 10.4210 · 6,336,350 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2dd8ecde32e7614ba12c1f383d5b03ae378a741c00a5c9da9d3f9addb2f61d17

View on Chainz ↗

Height

#459,935

Difficulty

10.420988

Transactions

Size

967 B

Version

Bits

0a6bc5dd

Nonce

215,539

Timestamp

3/25/2014, 3:35:06 PM

Confirmations

6,336,350

Mined by

⛏️ aS1VAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

558b432d1cae55fc34c13f609294cd2f76414e24068fc99c67a933240aba2305

Transactions (1)

Coinbase558b432d1cae55…a933240aba2305

1 in → 24 out9.1900 XPM879 B

AQvZBsUo…hppgRZTJ ATKK7iFz…wZm46KN1 ALqxX1WA…hsKjbnXn AJtNW28X…Syb4Ph5j AGKhfQo2…h7fBXLX6

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.

3.210 × 10⁹⁰(91-digit number)

32105883159741199604…31773358749015223679

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

3.210 × 10⁹⁰(91-digit number)

32105883159741199604…31773358749015223679

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.210 × 10⁹⁰(91-digit number)

32105883159741199604…31773358749015223681

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

6.421 × 10⁹⁰(91-digit number)

64211766319482399209…63546717498030447359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.421 × 10⁹⁰(91-digit number)

64211766319482399209…63546717498030447361

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

1.284 × 10⁹¹(92-digit number)

12842353263896479841…27093434996060894719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.284 × 10⁹¹(92-digit number)

12842353263896479841…27093434996060894721

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

2.568 × 10⁹¹(92-digit number)

25684706527792959683…54186869992121789439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.568 × 10⁹¹(92-digit number)

25684706527792959683…54186869992121789441

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

5.136 × 10⁹¹(92-digit number)

51369413055585919367…08373739984243578879

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.136 × 10⁹¹(92-digit number)

51369413055585919367…08373739984243578881

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