Block #231,688

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/28/2013, 3:22:04 PM · Difficulty 9.9404 · 6,564,990 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

39ab7cc1aa77820e68ae400667760a2d343adf42991bfd2a91d905c099bed2bc

View on Chainz ↗

Height

#231,688

Difficulty

9.940373

Transactions

Size

650 B

Version

Bits

09f0bc41

Nonce

607,393

Timestamp

10/28/2013, 3:22:04 PM

Confirmations

6,564,990

Mined by

⛏️ P2SHAXkXXDSonCmEEyyERk6LwYymWaQok2H6UF

Merkle Root

52721e93b941f8482cac203629d427c3378473678b390d2e5cbcdea553f530cc

Transactions (3)

Coinbasefcb7565174f5d3…8f1db4e66b5a53

1 in → 1 out10.1300 XPM109 B

AXkXXDSo…Qok2H6UF

bbc51b90cbd61e…61d28896630114

1 in → 2 out8.4400 XPM226 B

ARBgA31A…hV33BpP6 AeaR46Pf…gMi6bJB8

ff64bc9d3dede0…2cd6c1690eec22

1 in → 2 out3.7956 XPM225 B

AK7byDmv…K3he4dUG AcvKwvV4…dzrmx79J

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.

1.092 × 10⁹⁵(96-digit number)

10922003076869248043…54219668084763169199

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

1.092 × 10⁹⁵(96-digit number)

10922003076869248043…54219668084763169199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.092 × 10⁹⁵(96-digit number)

10922003076869248043…54219668084763169201

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

2.184 × 10⁹⁵(96-digit number)

21844006153738496087…08439336169526338399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.184 × 10⁹⁵(96-digit number)

21844006153738496087…08439336169526338401

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

4.368 × 10⁹⁵(96-digit number)

43688012307476992175…16878672339052676799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.368 × 10⁹⁵(96-digit number)

43688012307476992175…16878672339052676801

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

8.737 × 10⁹⁵(96-digit number)

87376024614953984350…33757344678105353599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.737 × 10⁹⁵(96-digit number)

87376024614953984350…33757344678105353601

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

1.747 × 10⁹⁶(97-digit number)

17475204922990796870…67514689356210707199

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