Block #488,296

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/12/2014, 3:28:37 PM · Difficulty 10.6521 · 6,329,707 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2beb57f91cfcf9319e79dd18f2e9c6c8bd1ca7555187b9a5b065b193338cf2db

View on Chainz ↗

Height

#488,296

Difficulty

10.652131

Transactions

Size

1.21 KB

Version

Bits

0aa6f208

Nonce

377,931

Timestamp

4/12/2014, 3:28:37 PM

Confirmations

6,329,707

Mined by

⛏️ hs5AdFLJFhbQJWBJcv1fjoDef6HbwbsaVkAyh

Merkle Root

a5cca5930ff32eea065aec82de3e314b37efbf4e566e2d4c31e9a2d18dfee18b

Transactions (2)

Coinbasedc8ad4d430803c…37502a666f5f1f

1 in → 21 out8.8100 XPM777 B

AdFLJFhb…bsaVkAyh AGz9gyZW…bo8NYQpw AMW1p9oT…2TzdaZxH AZ34NcPy…8FPeFjPV ASgUri65…C7NLcyBg

b3400a3ccf193e…0cd5452acb97e8

2 in → 2 out1.0337 XPM375 B

AWD9BEmD…FsuDtQdi AKEt9LSx…jcML1C46

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.

3.943 × 10⁹¹(92-digit number)

39433233260876296206…94240425126443330359

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

3.943 × 10⁹¹(92-digit number)

39433233260876296206…94240425126443330359

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.943 × 10⁹¹(92-digit number)

39433233260876296206…94240425126443330361

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

7.886 × 10⁹¹(92-digit number)

78866466521752592412…88480850252886660719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.886 × 10⁹¹(92-digit number)

78866466521752592412…88480850252886660721

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

1.577 × 10⁹²(93-digit number)

15773293304350518482…76961700505773321439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.577 × 10⁹²(93-digit number)

15773293304350518482…76961700505773321441

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

3.154 × 10⁹²(93-digit number)

31546586608701036964…53923401011546642879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.154 × 10⁹²(93-digit number)

31546586608701036964…53923401011546642881

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

6.309 × 10⁹²(93-digit number)

63093173217402073929…07846802023093285759

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.309 × 10⁹²(93-digit number)

63093173217402073929…07846802023093285761

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 #488,296

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