Block #245,472

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/5/2013, 11:59:10 AM · Difficulty 9.9639 · 6,569,507 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

605a5f306d9744bd98e3b5abc4df0fcfda12f4440f8af6cdabaeb706db4d0288

View on Chainz ↗

Height

#245,472

Difficulty

9.963895

Transactions

Size

1.61 KB

Version

Bits

09f6c1db

Nonce

75,155

Timestamp

11/5/2013, 11:59:10 AM

Confirmations

6,569,507

Mined by

⛏️ RxAJaGRnajU4FKPNSjrHvpAByLABiCHGoy6E

Merkle Root

2c7a248d98c2026ac33980690aa36470f437098d6413c347313e698b09c87839

Transactions (1)

Coinbase2c7a248d98c202…3e698b09c87839

1 in → 44 out10.0400 XPM1.52 KB

AJaGRnaj…iCHGoy6E ARpndEmc…Hg792kEk AMbCuLHZ…WSoStwkc AcEnwywz…vZtt2xTs AJzWx2VD…j4ZSMit5

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.

9.565 × 10⁸⁸(89-digit number)

95650260333401917195…85002610933308884019

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

9.565 × 10⁸⁸(89-digit number)

95650260333401917195…85002610933308884019

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.565 × 10⁸⁸(89-digit number)

95650260333401917195…85002610933308884021

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

1.913 × 10⁸⁹(90-digit number)

19130052066680383439…70005221866617768039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.913 × 10⁸⁹(90-digit number)

19130052066680383439…70005221866617768041

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

3.826 × 10⁸⁹(90-digit number)

38260104133360766878…40010443733235536079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.826 × 10⁸⁹(90-digit number)

38260104133360766878…40010443733235536081

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

7.652 × 10⁸⁹(90-digit number)

76520208266721533756…80020887466471072159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.652 × 10⁸⁹(90-digit number)

76520208266721533756…80020887466471072161

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

1.530 × 10⁹⁰(91-digit number)

15304041653344306751…60041774932942144319

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 #245,472

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