Block #464,034

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/28/2014, 12:58:01 PM · Difficulty 10.4164 · 6,346,093 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2acfeb5fe0302de88348207ef86345fc3bbe5d6e6de5c56bb770e7f3293e3fec

View on Chainz ↗

Height

#464,034

Difficulty

10.416372

Transactions

Size

5.58 KB

Version

Bits

0a6a9758

Nonce

18,755

Timestamp

3/28/2014, 12:58:01 PM

Confirmations

6,346,093

Mined by

⛏️ aAdFLJFhbQJWBJcv1fjoDef6HbwbsaVkAyh

Merkle Root

a4ead0198598bcfd804496ee22f61019f2afffc3f329d81bc5214965fb343629

Transactions (5)

Coinbasea4b295cf6658bf…f15fe54693926a

1 in → 21 out9.2800 XPM777 B

AdFLJFhb…bsaVkAyh AGz9gyZW…bo8NYQpw AbPcCMg4…719q6mAX ASgUri65…C7NLcyBg AbHY4iza…Yckt2J5W

ba89ab250bd23c…c7d84b696cfd17

1 in → 2 out9.1900 XPM226 B

AHeeFAQE…9Kf6SP5b AS4FJUwT…smxU8RwJ

ee99b623119842…fb6cdd6ba618a3

1 in → 2 out9.1900 XPM226 B

AP9CtVJc…YJQcZetr AW5nxX6F…c3tZzzHj

bf421a60cd4208…8e9f763dd69d11

1 in → 2 out9.1900 XPM225 B

AcMNnCDo…btimwL4a ARLDVtLn…1jdj6zES

a1b1b63c9e3513…a8f03bd258cc45

15 in → 57 out138.1100 XPM4.07 KB

APCzoU4y…kwX1GZVG AUkdqaxr…4jcbMUQ7 AKfwEQcv…uF2f3oRH AR8WV4KS…SChNuf3B ASqqpxAv…dTvgfRnF

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.

3.988 × 10⁹³(94-digit number)

39880937885703943741…65834489198179867419

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

3.988 × 10⁹³(94-digit number)

39880937885703943741…65834489198179867419

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.988 × 10⁹³(94-digit number)

39880937885703943741…65834489198179867421

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

7.976 × 10⁹³(94-digit number)

79761875771407887482…31668978396359734839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.976 × 10⁹³(94-digit number)

79761875771407887482…31668978396359734841

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

1.595 × 10⁹⁴(95-digit number)

15952375154281577496…63337956792719469679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.595 × 10⁹⁴(95-digit number)

15952375154281577496…63337956792719469681

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

3.190 × 10⁹⁴(95-digit number)

31904750308563154993…26675913585438939359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.190 × 10⁹⁴(95-digit number)

31904750308563154993…26675913585438939361

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

6.380 × 10⁹⁴(95-digit number)

63809500617126309986…53351827170877878719

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.380 × 10⁹⁴(95-digit number)

63809500617126309986…53351827170877878721

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 #464,034

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