Block #1,274,545

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 10/9/2015, 9:05:29 PM · Difficulty 10.8243 · 5,532,321 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

849f1c519237294e50e38f9abae7d551f87545708d4a8e812d22918786505254

View on Chainz ↗

Height

#1,274,545

Difficulty

10.824308

Transactions

Size

875 B

Version

Bits

0ad305d5

Nonce

94,413,469

Timestamp

10/9/2015, 9:05:29 PM

Confirmations

5,532,321

Mined by

⛏️ P2SHAJCEY9yyy2DERzsA24UUtHTMGPtg97E6zm

Merkle Root

dee317ae61a5887ad66290fb864a6f3c6c2948bb35d8eeb23578fb27f24fac79

Transactions (2)

Coinbasea1e1fbba5278f4…0048296dd10515

1 in → 1 out8.5300 XPM116 B

AJCEY9yy…tg97E6zm

79897479f6f289…d45a522a722e3f

1 in → 15 out19.7519 XPM668 B

AWhHG3cs…Qkg16jh4 ASG21nzq…iMYaGLq3 AGGC96kT…tgntK4X9 AYD7HpCq…GwGeTtcR AVtF3a7i…o8Hu62qE

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.

9.749 × 10⁹⁷(98-digit number)

97494375078566792616…82965419405975224319

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

9.749 × 10⁹⁷(98-digit number)

97494375078566792616…82965419405975224319

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.749 × 10⁹⁷(98-digit number)

97494375078566792616…82965419405975224321

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

1.949 × 10⁹⁸(99-digit number)

19498875015713358523…65930838811950448639

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.949 × 10⁹⁸(99-digit number)

19498875015713358523…65930838811950448641

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

3.899 × 10⁹⁸(99-digit number)

38997750031426717046…31861677623900897279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.899 × 10⁹⁸(99-digit number)

38997750031426717046…31861677623900897281

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

7.799 × 10⁹⁸(99-digit number)

77995500062853434093…63723355247801794559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.799 × 10⁹⁸(99-digit number)

77995500062853434093…63723355247801794561

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

1.559 × 10⁹⁹(100-digit number)

15599100012570686818…27446710495603589119

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.559 × 10⁹⁹(100-digit number)

15599100012570686818…27446710495603589121

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 #1,274,545

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