Block #479,128

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/7/2014, 12:37:36 PM · Difficulty 10.5000 · 6,328,791 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f8b4f59d0798f38a48b285ff71d8c1cc9c3668469b5ddfe83c39333d1069f1f3

View on Chainz ↗

Height

#479,128

Difficulty

10.499975

Transactions

Size

1.46 KB

Version

Bits

0a7ffe62

Nonce

101,540

Timestamp

4/7/2014, 12:37:36 PM

Confirmations

6,328,791

Mined by

⛏️ OaSBXAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

55784e29358f0ab98ca385ec02955a01ff87feef6e1def60cc7d191a1431e140

Transactions (2)

Coinbase86ef122e3695fe…2bda5d181e1049

1 in → 20 out9.0600 XPM743 B

AQvZBsUo…hppgRZTJ ANNg88pG…ppn21sTe AdxPNkWD…ZMa9u34q ATKK7iFz…wZm46KN1 AWMrD5hP…ZwsoxvZ3

6ea4968f06c24f…836a091b983120

3 in → 9 out27.3700 XPM658 B

ARKfDBQx…39urTKNS ALi2Y4yi…NcukCRyt Adg5BzYH…78vAFxLH ALsbU9Kz…C7sjAXyq AZwXBq4j…rzStTzBk

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.

2.332 × 10¹⁰⁴(105-digit number)

23326309611641762255…17759654269558118399

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

2.332 × 10¹⁰⁴(105-digit number)

23326309611641762255…17759654269558118399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.332 × 10¹⁰⁴(105-digit number)

23326309611641762255…17759654269558118401

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

4.665 × 10¹⁰⁴(105-digit number)

46652619223283524510…35519308539116236799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.665 × 10¹⁰⁴(105-digit number)

46652619223283524510…35519308539116236801

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

9.330 × 10¹⁰⁴(105-digit number)

93305238446567049021…71038617078232473599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.330 × 10¹⁰⁴(105-digit number)

93305238446567049021…71038617078232473601

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

1.866 × 10¹⁰⁵(106-digit number)

18661047689313409804…42077234156464947199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.866 × 10¹⁰⁵(106-digit number)

18661047689313409804…42077234156464947201

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

3.732 × 10¹⁰⁵(106-digit number)

37322095378626819608…84154468312929894399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.732 × 10¹⁰⁵(106-digit number)

37322095378626819608…84154468312929894401

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 #479,128

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