Block #125,983

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/20/2013, 2:29:30 PM · Difficulty 9.7789 · 6,668,476 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d62e7ed5ee7e22fb6bf58044b6a6ba344b0841552148072bc5726ee3bb1740a7

View on Chainz ↗

Height

#125,983

Difficulty

9.778905

Transactions

Size

689 B

Version

Bits

09c76658

Nonce

88,704

Timestamp

8/20/2013, 2:29:30 PM

Confirmations

6,668,476

Mined by

⛏️ P2SHAFwhRQTGAKmRCKhMrkfy9NQKioic8AshzD

Merkle Root

a68847a009a9a6438010f0da5b0122919f47c24f0b72f941f78830b1fc642fc5

Transactions (2)

Coinbase14d0e0458c618d…1428618f078335

1 in → 1 out10.4500 XPM109 B

AFwhRQTG…ic8AshzD

396d96740adc7a…9534245c1b917c

3 in → 1 out6.0141 XPM488 B

APBxWs9R…KTHWo3fT

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.

4.951 × 10⁹⁹(100-digit number)

49511132119462985001…68630574762248141239

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

4.951 × 10⁹⁹(100-digit number)

49511132119462985001…68630574762248141239

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.951 × 10⁹⁹(100-digit number)

49511132119462985001…68630574762248141241

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

9.902 × 10⁹⁹(100-digit number)

99022264238925970002…37261149524496282479

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.902 × 10⁹⁹(100-digit number)

99022264238925970002…37261149524496282481

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

1.980 × 10¹⁰⁰(101-digit number)

19804452847785194000…74522299048992564959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.980 × 10¹⁰⁰(101-digit number)

19804452847785194000…74522299048992564961

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

3.960 × 10¹⁰⁰(101-digit number)

39608905695570388000…49044598097985129919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.960 × 10¹⁰⁰(101-digit number)

39608905695570388000…49044598097985129921

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

7.921 × 10¹⁰⁰(101-digit number)

79217811391140776001…98089196195970259839

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