Block #145,412

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 9/1/2013, 9:19:36 PM · Difficulty 9.8441 · 6,646,078 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3ae083420965343babcef43a32a9d431dc2e787883773c95e4b21c5d3291eb05

View on Chainz ↗

Height

#145,412

Difficulty

9.844072

Transactions

Size

797 B

Version

Bits

09d81518

Nonce

451,290

Timestamp

9/1/2013, 9:19:36 PM

Confirmations

6,646,078

Merkle Root

69f405d256dabb78340cd4dce993e717615c4a33523d981198911f3b36d20b60

Transactions (3)

Coinbased45be32ce286d5…5b9788d0db71fe

1 in → 1 out10.3200 XPM109 B

APEcDKBh…bvmts2ty

956bc8c02764e4…b4a1f165fb1d33

1 in → 2 out2.2076 XPM226 B

AJNNAhp6…Yx382eYG ANvr2nC2…rH18gE4w

675059cd925ea9…e094f04b2b9c21

2 in → 2 out2.0605 XPM373 B

ARXSrG7z…CRW69WR4 ALp3yhdv…snv6YY3Y

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.

1.522 × 10⁹³(94-digit number)

15229183698945040639…67902769893925641279

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

1.522 × 10⁹³(94-digit number)

15229183698945040639…67902769893925641279

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.522 × 10⁹³(94-digit number)

15229183698945040639…67902769893925641281

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

3.045 × 10⁹³(94-digit number)

30458367397890081278…35805539787851282559

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.045 × 10⁹³(94-digit number)

30458367397890081278…35805539787851282561

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

6.091 × 10⁹³(94-digit number)

60916734795780162557…71611079575702565119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.091 × 10⁹³(94-digit number)

60916734795780162557…71611079575702565121

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

1.218 × 10⁹⁴(95-digit number)

12183346959156032511…43222159151405130239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.218 × 10⁹⁴(95-digit number)

12183346959156032511…43222159151405130241

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

2.436 × 10⁹⁴(95-digit number)

24366693918312065023…86444318302810260479

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