Block #291,177

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 12/3/2013, 1:23:09 AM · Difficulty 9.9897 · 6,518,455 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

9a004cd93401693a82fd425af7e65d0ab3c73aac40e9609001ed34969c058c5c

View on Chainz ↗

Height

#291,177

Difficulty

9.989710

Transactions

Size

969 B

Version

Bits

09fd5da3

Nonce

97,877

Timestamp

12/3/2013, 1:23:09 AM

Confirmations

6,518,455

Mined by

⛏️ iqaR2,AZninDSu1Gy3NdWkaTGfLDa2i9FvgDMwC4

Merkle Root

4d93185631f1ae30a3a41ce2136d820283661b035bd917337385b443985d3bb4

Transactions (1)

Coinbase4d93185631f1ae…85b443985d3bb4

1 in → 24 out10.0100 XPM879 B

AZninDSu…FvgDMwC4 AXKzpTxE…apdEL1zM AGCXewgR…nPX52WFq AYcLTeXR…bscgPops AeXR4zCu…M3JoUyt8

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.

9.292 × 10⁹⁴(95-digit number)

92921154170887535488…02821604321536333499

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

9.292 × 10⁹⁴(95-digit number)

92921154170887535488…02821604321536333499

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.292 × 10⁹⁴(95-digit number)

92921154170887535488…02821604321536333501

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

1.858 × 10⁹⁵(96-digit number)

18584230834177507097…05643208643072666999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.858 × 10⁹⁵(96-digit number)

18584230834177507097…05643208643072667001

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

3.716 × 10⁹⁵(96-digit number)

37168461668355014195…11286417286145333999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.716 × 10⁹⁵(96-digit number)

37168461668355014195…11286417286145334001

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

7.433 × 10⁹⁵(96-digit number)

74336923336710028390…22572834572290667999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.433 × 10⁹⁵(96-digit number)

74336923336710028390…22572834572290668001

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

1.486 × 10⁹⁶(97-digit number)

14867384667342005678…45145669144581335999

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 #291,177

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