Block #307,375

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/12/2013, 1:18:51 PM · Difficulty 9.9942 · 6,502,379 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8ff7a78dd15a546ef9242853916060402bb79a9190713588e56bdd63753533fa

View on Chainz ↗

Height

#307,375

Difficulty

9.994175

Transactions

Size

1.54 KB

Version

Bits

09fe8243

Nonce

56,448

Timestamp

12/12/2013, 1:18:51 PM

Confirmations

6,502,379

Mined by

⛏️ P2SHAUUsuND8AN3pwVQnVzvvqN8LwL8aToVvPX

Merkle Root

3ebb45068a7e25dfb7136d48c6c9574ba5e19442d9541ac62c2f738ade136ef4

Transactions (5)

Coinbase7c58ebcb6d1165…85409c297d3f17

1 in → 1 out10.0453 XPM109 B

AUUsuND8…8aToVvPX

fdcd8e50b5595c…f1ec77c4d4d8ec

1 in → 1 out59.9900 XPM192 B

ANnw5MpX…VoVX6Bzi

a4b5f2d9dfcaee…84ba3fffe88c4f

1 in → 1 out10.0100 XPM157 B

AcxihRF5…yPzP9VNh

180a31eaa859e4…c0f5894ed8ced1

3 in → 10 out30.4200 XPM693 B

AX12m5ft…Z5FUZS4F APq3LH2A…koKKWWN9 AeKNrjNj…1NEq95Ta AejJS756…87uMVBzT AcyKdXFh…EUAbfEQB

3d461552ccf3c9…3cce5a00f082e3

2 in → 1 out2.0000 XPM340 B

AM4Jc3k1…VkewjYj1

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.

2.784 × 10⁹⁶(97-digit number)

27846424318896006975…82893868495086239999

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

2.784 × 10⁹⁶(97-digit number)

27846424318896006975…82893868495086239999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.784 × 10⁹⁶(97-digit number)

27846424318896006975…82893868495086240001

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

5.569 × 10⁹⁶(97-digit number)

55692848637792013950…65787736990172479999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.569 × 10⁹⁶(97-digit number)

55692848637792013950…65787736990172480001

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

1.113 × 10⁹⁷(98-digit number)

11138569727558402790…31575473980344959999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.113 × 10⁹⁷(98-digit number)

11138569727558402790…31575473980344960001

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

2.227 × 10⁹⁷(98-digit number)

22277139455116805580…63150947960689919999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.227 × 10⁹⁷(98-digit number)

22277139455116805580…63150947960689920001

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

4.455 × 10⁹⁷(98-digit number)

44554278910233611160…26301895921379839999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.455 × 10⁹⁷(98-digit number)

44554278910233611160…26301895921379840001

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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 #307,375

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