Block #124,597

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/19/2013, 6:09:08 PM · Difficulty 9.7715 · 6,689,284 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

5b45da2e8644008e00e8b1827c260f9488b875237ab142bf22929b14a970fc7d

View on Chainz ↗

Height

#124,597

Difficulty

9.771469

Transactions

Size

426 B

Version

Bits

09c57f01

Nonce

166,731

Timestamp

8/19/2013, 6:09:08 PM

Confirmations

6,689,284

Mined by

⛏️ P2SHAKaGDwVVv7VLKh2cmLacAjw2bVh5Bk5GFu

Merkle Root

473258d05945ca57e1a23cf24ab57139cf2742c0e63b6c5167517b23169c8163

Transactions (2)

Coinbase5103dce1e287dc…ac63610fa23d90

1 in → 1 out10.4700 XPM109 B

AKaGDwVV…h5Bk5GFu

9acb920b832fc3…2d4bf361940ba8

1 in → 2 out2.0110 XPM226 B

AUnbEDhc…XyWWnLdS ANUQordU…HmvbBhff

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.

7.383 × 10⁹⁷(98-digit number)

73837831064571810079…18781929371200909339

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

7.383 × 10⁹⁷(98-digit number)

73837831064571810079…18781929371200909339

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.383 × 10⁹⁷(98-digit number)

73837831064571810079…18781929371200909341

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

1.476 × 10⁹⁸(99-digit number)

14767566212914362015…37563858742401818679

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.476 × 10⁹⁸(99-digit number)

14767566212914362015…37563858742401818681

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

2.953 × 10⁹⁸(99-digit number)

29535132425828724031…75127717484803637359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.953 × 10⁹⁸(99-digit number)

29535132425828724031…75127717484803637361

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

5.907 × 10⁹⁸(99-digit number)

59070264851657448063…50255434969607274719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.907 × 10⁹⁸(99-digit number)

59070264851657448063…50255434969607274721

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

1.181 × 10⁹⁹(100-digit number)

11814052970331489612…00510869939214549439

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

Block #124,597

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