Block #231,687

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/28/2013, 3:20:48 PM · Difficulty 9.9404 · 6,563,929 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

65fdc73b26827e8c7af011072352e57663c4d282bbe6c3216193f613037db798

View on Chainz ↗

Height

#231,687

Difficulty

9.940367

Transactions

Size

429 B

Version

Bits

09f0bbe4

Nonce

2,797

Timestamp

10/28/2013, 3:20:48 PM

Confirmations

6,563,929

Mined by

⛏️ P2SHAHFusNobK5sbH79QmVs3atiakRQHvWJq8X

Merkle Root

86ad52dbbbb5cda4ef178dbd9bc0c1ce19c109a0f23bb1eeeb7353295e2d75ae

Transactions (2)

Coinbase9d16dce6467e2e…90002f7c0e4896

1 in → 2 out10.1200 XPM147 B

AHFusNob…QHvWJq8X Abiw8n3q…ZnZfgvQW

76397d8a3dcf0d…965184f56e3688

1 in → 2 out10.1400 XPM192 B

Abp4JYsb…5EMRrVvY ANV6D3KX…Lnjn3pZX

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.

4.981 × 10⁹⁵(96-digit number)

49812539257717534836…19693393939291165119

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

4.981 × 10⁹⁵(96-digit number)

49812539257717534836…19693393939291165119

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.981 × 10⁹⁵(96-digit number)

49812539257717534836…19693393939291165121

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

9.962 × 10⁹⁵(96-digit number)

99625078515435069673…39386787878582330239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.962 × 10⁹⁵(96-digit number)

99625078515435069673…39386787878582330241

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

1.992 × 10⁹⁶(97-digit number)

19925015703087013934…78773575757164660479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.992 × 10⁹⁶(97-digit number)

19925015703087013934…78773575757164660481

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

3.985 × 10⁹⁶(97-digit number)

39850031406174027869…57547151514329320959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.985 × 10⁹⁶(97-digit number)

39850031406174027869…57547151514329320961

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

7.970 × 10⁹⁶(97-digit number)

79700062812348055738…15094303028658641919

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