Block #359,256

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/14/2014, 3:57:17 PM · Difficulty 10.3879 · 6,480,576 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

13fc4425e30e6593ac717e474bcf708de2105340bccf04759d3f80d9d4ad7852

View on Chainz ↗

Height

#359,256

Difficulty

10.387910

Transactions

Size

1.15 KB

Version

Bits

0a634e0a

Nonce

32,533

Timestamp

1/14/2014, 3:57:17 PM

Confirmations

6,480,576

Mined by

⛏️ P2SHAGKsuwkXLS3wAfkf3stugCwV3eP6QrncHa

Merkle Root

8d666aec049f9a9fa0708cf2fc2091e807f68b29620278df065d1d2fa5cf6d55

Transactions (4)

Coinbasedb867c9907f9b4…22ef5241389980

1 in → 1 out9.2800 XPM109 B

AGKsuwkX…P6QrncHa

9751b4d1deb40e…71292a0334fa77

1 in → 2 out5.1508 XPM227 B

ARXirURT…igtvScRu AbNDwnZv…65mPtpPA

01922eb907cde7…d0b6bd1ee61e91

1 in → 2 out5.2268 XPM226 B

AGJp6RTh…nR3iamGg Ado1W2jf…YbjVbPU6

27a5c9b5b76a84…b9c432db606089

3 in → 2 out1.0675 XPM523 B

AGusNSbi…TMhj3ShN AUyADfh9…aVXcsyf7

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.

8.028 × 10⁹⁸(99-digit number)

80285629101486717010…34631248507478081839

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

8.028 × 10⁹⁸(99-digit number)

80285629101486717010…34631248507478081839

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.028 × 10⁹⁸(99-digit number)

80285629101486717010…34631248507478081841

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

1.605 × 10⁹⁹(100-digit number)

16057125820297343402…69262497014956163679

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.605 × 10⁹⁹(100-digit number)

16057125820297343402…69262497014956163681

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

3.211 × 10⁹⁹(100-digit number)

32114251640594686804…38524994029912327359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.211 × 10⁹⁹(100-digit number)

32114251640594686804…38524994029912327361

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

6.422 × 10⁹⁹(100-digit number)

64228503281189373608…77049988059824654719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.422 × 10⁹⁹(100-digit number)

64228503281189373608…77049988059824654721

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

1.284 × 10¹⁰⁰(101-digit number)

12845700656237874721…54099976119649309439

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.284 × 10¹⁰⁰(101-digit number)

12845700656237874721…54099976119649309441

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 #359,256

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