Block #478,688

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/7/2014, 6:01:56 AM · Difficulty 10.4954 · 6,348,465 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a07b4a971290101bac609d1548e930792b041258e6d28b151cab0bc3b1823183

View on Chainz ↗

Height

#478,688

Difficulty

10.495405

Transactions

Size

1.28 KB

Version

Bits

0a7ed2da

Nonce

2,444

Timestamp

4/7/2014, 6:01:56 AM

Confirmations

6,348,465

Mined by

⛏️ MFAMVf7JrgD9LEuSS2R27DgQAdb3xd5AVR7C

Merkle Root

608a27bbf98f536757acc9c77f4a330e2ac19e4310b0f01c9faa960bf974fdee

Transactions (5)

Coinbase02b561440a0d1b…3f3721fc4ed857

1 in → 3 out9.1000 XPM165 B

AMVf7Jrg…xd5AVR7C ALzzzbUz…2Cb4jSDN AJno7LX2…vo4wdWtY

d928328e5f2f23…74f898e4534372

1 in → 2 out5.5737 XPM226 B

AP9CtVJc…YJQcZetr ATDFvhJo…DNJViZX4

10fe3e748dbbb2…cdaee691119a43

1 in → 2 out4.5037 XPM226 B

ASfQj9Pb…Q87HBF2g AdCqHTnu…FANDk59L

ef8f6251e15118…e0452c2c317bb1

1 in → 2 out3.0189 XPM226 B

APZhgoxg…vikX3isc AFquV6pg…7FRWyPoK

2dd561861ac47e…51d822e2fb506a

2 in → 2 out1.0800 XPM375 B

AQiG9TF4…Gs8Bnynw AXnL68UR…jsxeGUhN

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.

6.305 × 10⁹⁸(99-digit number)

63057145789249358847…66844670389406719999

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

6.305 × 10⁹⁸(99-digit number)

63057145789249358847…66844670389406719999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.305 × 10⁹⁸(99-digit number)

63057145789249358847…66844670389406720001

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

1.261 × 10⁹⁹(100-digit number)

12611429157849871769…33689340778813439999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.261 × 10⁹⁹(100-digit number)

12611429157849871769…33689340778813440001

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

2.522 × 10⁹⁹(100-digit number)

25222858315699743538…67378681557626879999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.522 × 10⁹⁹(100-digit number)

25222858315699743538…67378681557626880001

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

5.044 × 10⁹⁹(100-digit number)

50445716631399487077…34757363115253759999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.044 × 10⁹⁹(100-digit number)

50445716631399487077…34757363115253760001

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

1.008 × 10¹⁰⁰(101-digit number)

10089143326279897415…69514726230507519999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.008 × 10¹⁰⁰(101-digit number)

10089143326279897415…69514726230507520001

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 #478,688

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