Block #93,232

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/2/2013, 7:14:47 AM · Difficulty 9.1948 · 6,705,586 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

cf4ee6c315e067e53efb2bb6724233bdcbb8aaee6785ac13d7a6de5ec51a93fc

View on Chainz ↗

Height

#93,232

Difficulty

9.194812

Transactions

Size

547 B

Version

Bits

0931df36

Nonce

653,101

Timestamp

8/2/2013, 7:14:47 AM

Confirmations

6,705,586

Mined by

⛏️ P2SHAJwT4t7mqNZ7nwyuBKJTxL3n2nrXZrFS9k

Merkle Root

f124cc35f23fd170ac3f9e5a1b51c412a2321ffc7200dfe0383c1c2bc0e9aa23

Transactions (2)

Coinbase0cadbccf3b4f27…dc74a47059f2e8

1 in → 1 out11.8200 XPM109 B

AJwT4t7m…rXZrFS9k

137197f5e0f96c…1af6e4ec3c7f1f

2 in → 1 out174.9900 XPM340 B

AJV9J7t5…G9F5PrK8

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.

9.525 × 10¹¹⁴(115-digit number)

95256259874972151742…69854147289395636419

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

9.525 × 10¹¹⁴(115-digit number)

95256259874972151742…69854147289395636419

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.525 × 10¹¹⁴(115-digit number)

95256259874972151742…69854147289395636421

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

1.905 × 10¹¹⁵(116-digit number)

19051251974994430348…39708294578791272839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.905 × 10¹¹⁵(116-digit number)

19051251974994430348…39708294578791272841

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

3.810 × 10¹¹⁵(116-digit number)

38102503949988860697…79416589157582545679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.810 × 10¹¹⁵(116-digit number)

38102503949988860697…79416589157582545681

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

7.620 × 10¹¹⁵(116-digit number)

76205007899977721394…58833178315165091359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.620 × 10¹¹⁵(116-digit number)

76205007899977721394…58833178315165091361

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

1.524 × 10¹¹⁶(117-digit number)

15241001579995544278…17666356630330182719

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