Block #478,238

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/6/2014, 11:07:10 PM · Difficulty 10.4915 · 6,328,488 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

cfe03e2f2058da811715c0b15f15f01954d9b9d1a1aada1f209b99ebf15e9293

View on Chainz ↗

Height

#478,238

Difficulty

10.491544

Transactions

Size

3.24 KB

Version

Bits

0a7dd5ce

Nonce

45,117,780

Timestamp

4/6/2014, 11:07:10 PM

Confirmations

6,328,488

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

36a5b8360a78f0e6ab4e18eaae7f2d892ea87acf8de511399ed8dfc6c18bc8e8

Transactions (3)

Coinbase0f8eafee67050d…99846fc4dc105b

1 in → 1 out9.1100 XPM116 B

AbwWkWZt…kawDhufa

893c64a1faace4…2be3f48b9ef38f

19 in → 2 out5.4638 XPM2.82 KB

ATzNqULc…5WQcwDbE APnMqt5P…dUqAqJ1a

e87d68f983f42b…0e0c39dab05f7c

1 in → 2 out7.5892 XPM226 B

ALvkrjP2…4SmTh6LC Aeuc3WSZ…ythjLmc9

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.

3.982 × 10⁹⁷(98-digit number)

39821654992719767626…47499956837535440639

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

3.982 × 10⁹⁷(98-digit number)

39821654992719767626…47499956837535440639

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.982 × 10⁹⁷(98-digit number)

39821654992719767626…47499956837535440641

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

7.964 × 10⁹⁷(98-digit number)

79643309985439535252…94999913675070881279

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.964 × 10⁹⁷(98-digit number)

79643309985439535252…94999913675070881281

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

1.592 × 10⁹⁸(99-digit number)

15928661997087907050…89999827350141762559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.592 × 10⁹⁸(99-digit number)

15928661997087907050…89999827350141762561

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

3.185 × 10⁹⁸(99-digit number)

31857323994175814101…79999654700283525119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.185 × 10⁹⁸(99-digit number)

31857323994175814101…79999654700283525121

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

6.371 × 10⁹⁸(99-digit number)

63714647988351628202…59999309400567050239

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.371 × 10⁹⁸(99-digit number)

63714647988351628202…59999309400567050241

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 #478,238

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