Block #291,525

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 12/3/2013, 5:49:51 AM · Difficulty 9.9899 · 6,522,790 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

700df9991426e03e2b2ba5905fd019b010831583bf7f3cc984062e895cc9649c

View on Chainz ↗

Height

#291,525

Difficulty

9.989888

Transactions

Size

944 B

Version

Bits

09fd694a

Nonce

72,730

Timestamp

12/3/2013, 5:49:51 AM

Confirmations

6,522,790

Mined by

⛏️ P2SHALgvhYRJikQ3YBgLuDzfeCRKix1KZX33Xo

Merkle Root

0b9c629cd2055f3505d133b08f0a7c203ff26d4920815f3c9f6bb069a40ac35b

Transactions (3)

Coinbase9810ac361a619c…368893be63e015

1 in → 1 out10.0300 XPM109 B

ALgvhYRJ…1KZX33Xo

2eb8b9709dd67a…ceb1439c23f197

1 in → 2 out0.9900 XPM226 B

ALihSRNE…giTd8JPy AUh5kG9s…UrMcYyt4

f7de226861bffc…6f454e53234b06

3 in → 2 out1.1051 XPM521 B

AVPw6F6J…YKfrQomU AcDKAHmJ…ZGLUf4rV

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.

1.862 × 10⁹⁰(91-digit number)

18626153337945548293…47227599728604421999

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

1.862 × 10⁹⁰(91-digit number)

18626153337945548293…47227599728604421999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.862 × 10⁹⁰(91-digit number)

18626153337945548293…47227599728604422001

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

3.725 × 10⁹⁰(91-digit number)

37252306675891096587…94455199457208843999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.725 × 10⁹⁰(91-digit number)

37252306675891096587…94455199457208844001

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

7.450 × 10⁹⁰(91-digit number)

74504613351782193174…88910398914417687999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.450 × 10⁹⁰(91-digit number)

74504613351782193174…88910398914417688001

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

1.490 × 10⁹¹(92-digit number)

14900922670356438634…77820797828835375999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.490 × 10⁹¹(92-digit number)

14900922670356438634…77820797828835376001

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

2.980 × 10⁹¹(92-digit number)

29801845340712877269…55641595657670751999

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 #291,525

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