Block #606,709

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 6/29/2014, 12:00:33 PM · Difficulty 10.9075 · 6,196,919 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

7043beb11a4e28ef508a7357f62d440bc135c351235664cc5d3a86b55b5d72ac

View on Chainz ↗

Height

#606,709

Difficulty

10.907496

Transactions

Size

662 B

Version

Bits

0ae851a4

Nonce

58,644

Timestamp

6/29/2014, 12:00:33 PM

Confirmations

6,196,919

Mined by

⛏️ AAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

a88ac9699b359a078da647e02f6f2bd2042d1a8320c4fcbf3cf164ce7a7bf554

Transactions (1)

Coinbasea88ac9699b359a…f164ce7a7bf554

1 in → 15 out8.3900 XPM573 B

AQvZBsUo…hppgRZTJ AJzWx2VD…j4ZSMit5 AJtNW28X…Syb4Ph5j AQyr8Lw3…hs4nt3Pn AbAntGri…qDcFrazz

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.

2.475 × 10⁹³(94-digit number)

24753699362591280092…62733057969821845119

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

2.475 × 10⁹³(94-digit number)

24753699362591280092…62733057969821845119

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.475 × 10⁹³(94-digit number)

24753699362591280092…62733057969821845121

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

4.950 × 10⁹³(94-digit number)

49507398725182560185…25466115939643690239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.950 × 10⁹³(94-digit number)

49507398725182560185…25466115939643690241

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

9.901 × 10⁹³(94-digit number)

99014797450365120371…50932231879287380479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.901 × 10⁹³(94-digit number)

99014797450365120371…50932231879287380481

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

1.980 × 10⁹⁴(95-digit number)

19802959490073024074…01864463758574760959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.980 × 10⁹⁴(95-digit number)

19802959490073024074…01864463758574760961

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

3.960 × 10⁹⁴(95-digit number)

39605918980146048148…03728927517149521919

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.960 × 10⁹⁴(95-digit number)

39605918980146048148…03728927517149521921

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