Block #610,749

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 7/1/2014, 8:57:39 PM · Difficulty 10.9184 · 6,199,455 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

44154c0b195ebb966ae0cf5f3c571eceefafb44ac579182d223652987b64ff6a

View on Chainz ↗

Height

#610,749

Difficulty

10.918405

Transactions

Size

1.45 KB

Version

Bits

0aeb1c92

Nonce

6,765,665

Timestamp

7/1/2014, 8:57:39 PM

Confirmations

6,199,455

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

daea5855f7f9c6607261187d50399ac0834e28b454e10762f93eb8648b9d5ad6

Transactions (4)

Coinbase3f21d46d085332…482f47f98c8039

1 in → 1 out8.4100 XPM116 B

ANSXnLY2…Sd25TjkD

550f61f4f82e1d…0d762d0300f994

1 in → 2 out8.3700 XPM226 B

Aanx8jRu…9DsLhXZv AW7k2MZd…9b8YznyG

fe5d2290670438…bca7b0908e4186

5 in → 2 out39.8569 XPM820 B

AdcG2pvT…Pnacq5vF AJofcPVi…KaTgbzFV

e24acbd7f21c3f…3740cef81aa66b

1 in → 2 out6.3438 XPM227 B

AYUoHzUr…kiG1KKa5 AYrwBKyU…1S6w2wRP

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.

8.916 × 10⁹⁵(96-digit number)

89163155670509653517…12311585599912511679

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

8.916 × 10⁹⁵(96-digit number)

89163155670509653517…12311585599912511679

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.916 × 10⁹⁵(96-digit number)

89163155670509653517…12311585599912511681

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

1.783 × 10⁹⁶(97-digit number)

17832631134101930703…24623171199825023359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.783 × 10⁹⁶(97-digit number)

17832631134101930703…24623171199825023361

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

3.566 × 10⁹⁶(97-digit number)

35665262268203861407…49246342399650046719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.566 × 10⁹⁶(97-digit number)

35665262268203861407…49246342399650046721

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

7.133 × 10⁹⁶(97-digit number)

71330524536407722814…98492684799300093439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.133 × 10⁹⁶(97-digit number)

71330524536407722814…98492684799300093441

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

1.426 × 10⁹⁷(98-digit number)

14266104907281544562…96985369598600186879

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.426 × 10⁹⁷(98-digit number)

14266104907281544562…96985369598600186881

Verify on FactorDB ↗Wolfram Alpha ↗

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

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

2.853 × 10⁹⁷(98-digit number)

28532209814563089125…93970739197200373759

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 #610,749

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