Block #177,578

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 9/23/2013, 6:44:21 PM · Difficulty 9.8643 · 6,613,627 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

4b329344671efbc00215fb63776f6b5c4223ce7528ea4f1d7b40c80c37357a76

View on Chainz ↗

Height

#177,578

Difficulty

9.864276

Transactions

Size

9.28 KB

Version

Bits

09dd4138

Nonce

73,217

Timestamp

9/23/2013, 6:44:21 PM

Confirmations

6,613,627

Merkle Root

e5c27dc2fb5b1b5a1cc0a6a997fe4ea33d0132a30401c2556d201f3a024c8d21

Transactions (2)

Coinbasee2d64a0c795bc5…23265e77548f23

1 in → 1 out10.3600 XPM109 B

AcDoNL3w…ViN23bk2

420ce00cea766f…ff692e646689c3

80 in → 2 out8007.9260 XPM9.09 KB

AVya9PoB…Sxjginfx APiUcRYP…MWiGmTvq

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.

1.705 × 10¹⁰⁰(101-digit number)

17051568769402478949…35322709485145185599

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

1.705 × 10¹⁰⁰(101-digit number)

17051568769402478949…35322709485145185599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.705 × 10¹⁰⁰(101-digit number)

17051568769402478949…35322709485145185601

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

3.410 × 10¹⁰⁰(101-digit number)

34103137538804957898…70645418970290371199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.410 × 10¹⁰⁰(101-digit number)

34103137538804957898…70645418970290371201

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

6.820 × 10¹⁰⁰(101-digit number)

68206275077609915797…41290837940580742399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.820 × 10¹⁰⁰(101-digit number)

68206275077609915797…41290837940580742401

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

1.364 × 10¹⁰¹(102-digit number)

13641255015521983159…82581675881161484799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.364 × 10¹⁰¹(102-digit number)

13641255015521983159…82581675881161484801

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

2.728 × 10¹⁰¹(102-digit number)

27282510031043966318…65163351762322969599

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