Block #483,415

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/10/2014, 1:20:00 AM · Difficulty 10.5615 · 6,341,086 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e5ab2da57041ec55ff9c482df8cde3efa5202d6b31c705afc0c41b7c67d24200

View on Chainz ↗

Height

#483,415

Difficulty

10.561490

Transactions

Size

15.61 KB

Version

Bits

0a8fbdca

Nonce

33,557,390

Timestamp

4/10/2014, 1:20:00 AM

Confirmations

6,341,086

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

65010f17c49916deaac1c46ac1d28026ad5011521e2385b1e610d708fedabd8c

Transactions (4)

Coinbase63af6d1042b6af…7860957db3f86e

1 in → 1 out9.1300 XPM116 B

AbwWkWZt…kawDhufa

f1a46c05ad68a5…75fac7ff577df1

5 in → 2 out9.9101 XPM818 B

APpkkona…8QpJbacp AKkk5qo5…SZCThhf8

7669a7b00985d7…ab29d4a7bdd557

70 in → 2 out50.0100 XPM10.19 KB

AJME8fpz…SV7y9UwA AXueG7w9…gHdeyZR1

93851c00cf6b62…ceb08fb0dd88bd

30 in → 2 out30.6338 XPM4.41 KB

Adtz29hE…BDApjg1K AZSjhnMj…Mnf3y9ki

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.

5.292 × 10⁹⁸(99-digit number)

52927071117537309163…01816921891950258999

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

5.292 × 10⁹⁸(99-digit number)

52927071117537309163…01816921891950258999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.292 × 10⁹⁸(99-digit number)

52927071117537309163…01816921891950259001

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

1.058 × 10⁹⁹(100-digit number)

10585414223507461832…03633843783900517999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.058 × 10⁹⁹(100-digit number)

10585414223507461832…03633843783900518001

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

2.117 × 10⁹⁹(100-digit number)

21170828447014923665…07267687567801035999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.117 × 10⁹⁹(100-digit number)

21170828447014923665…07267687567801036001

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

4.234 × 10⁹⁹(100-digit number)

42341656894029847330…14535375135602071999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.234 × 10⁹⁹(100-digit number)

42341656894029847330…14535375135602072001

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

8.468 × 10⁹⁹(100-digit number)

84683313788059694661…29070750271204143999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.468 × 10⁹⁹(100-digit number)

84683313788059694661…29070750271204144001

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 #483,415

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