Block #449,991

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/18/2014, 11:54:44 PM · Difficulty 10.3706 · 6,374,838 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

0929115ac2744b67b2f4911ed1834319ee61392fb65956982cf475361f05fe81

View on Chainz ↗

Height

#449,991

Difficulty

10.370624

Transactions

Size

401 B

Version

Bits

0a5ee13b

Nonce

337,930

Timestamp

3/18/2014, 11:54:44 PM

Confirmations

6,374,838

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

05711fec5fe030e82971016c391e921cfecf7f7b47e9196c46eea3ac75f9d7fb

Transactions (2)

Coinbase378572072d47d3…49da34961d6a26

1 in → 1 out9.2905 XPM116 B

AbwWkWZt…kawDhufa

8ed8f7fb05fa4d…0f9f09bd60a818

1 in → 1 out3.2790 XPM192 B

AW5M7U6Z…6fFdhffy

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.

5.774 × 10¹⁰²(103-digit number)

57745433295705918817…72966717813517829119

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

5.774 × 10¹⁰²(103-digit number)

57745433295705918817…72966717813517829119

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.774 × 10¹⁰²(103-digit number)

57745433295705918817…72966717813517829121

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

1.154 × 10¹⁰³(104-digit number)

11549086659141183763…45933435627035658239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.154 × 10¹⁰³(104-digit number)

11549086659141183763…45933435627035658241

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

2.309 × 10¹⁰³(104-digit number)

23098173318282367526…91866871254071316479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.309 × 10¹⁰³(104-digit number)

23098173318282367526…91866871254071316481

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

4.619 × 10¹⁰³(104-digit number)

46196346636564735053…83733742508142632959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.619 × 10¹⁰³(104-digit number)

46196346636564735053…83733742508142632961

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

9.239 × 10¹⁰³(104-digit number)

92392693273129470107…67467485016285265919

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.239 × 10¹⁰³(104-digit number)

92392693273129470107…67467485016285265921

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

Block #449,991

Cookie Preferences