Block #491,031

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/14/2014, 6:01:44 AM · Difficulty 10.6802 · 6,317,405 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d77c3956756be7714ab45f48fa4beade5f5d52f3b1804c9f586d4aa162188ab7

View on Chainz ↗

Height

#491,031

Difficulty

10.680206

Transactions

Size

658 B

Version

Bits

0aae21ff

Nonce

72,238,505

Timestamp

4/14/2014, 6:01:44 AM

Confirmations

6,317,405

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

90bd673d1e1ad8cdba5f168405c3279fb2fceb44bfc2cf848e2405df468e66db

Transactions (3)

Coinbase64cfe19ddd8212…0cc4a3ad497ef8

1 in → 1 out8.7700 XPM116 B

AbwWkWZt…kawDhufa

bd7937b3c54c5f…a146e83a832de3

1 in → 2 out5.2080 XPM225 B

AHRSa1Mg…YZd9E3ZY AerrjcNc…QPu2sGrj

83611404f31924…d1caf4f8b6a3c7

1 in → 2 out2.7702 XPM226 B

AcvBcnB4…yEUgjERG Aaffr4EL…bJQCxKCY

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.

2.835 × 10⁹⁷(98-digit number)

28352800467398904196…11662641642074088579

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

2.835 × 10⁹⁷(98-digit number)

28352800467398904196…11662641642074088579

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.835 × 10⁹⁷(98-digit number)

28352800467398904196…11662641642074088581

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

5.670 × 10⁹⁷(98-digit number)

56705600934797808392…23325283284148177159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.670 × 10⁹⁷(98-digit number)

56705600934797808392…23325283284148177161

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

1.134 × 10⁹⁸(99-digit number)

11341120186959561678…46650566568296354319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.134 × 10⁹⁸(99-digit number)

11341120186959561678…46650566568296354321

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

2.268 × 10⁹⁸(99-digit number)

22682240373919123357…93301133136592708639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.268 × 10⁹⁸(99-digit number)

22682240373919123357…93301133136592708641

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

4.536 × 10⁹⁸(99-digit number)

45364480747838246714…86602266273185417279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.536 × 10⁹⁸(99-digit number)

45364480747838246714…86602266273185417281

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 #491,031

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