Block #489,453

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/13/2014, 7:30:46 AM · Difficulty 10.6652 · 6,319,958 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

106bcc777d184aa02c06b916d1a9ce510dff48d628eb9e7c5ba02869e2e2a0b6

View on Chainz ↗

Height

#489,453

Difficulty

10.665188

Transactions

Size

834 B

Version

Bits

0aaa49cb

Nonce

99,533

Timestamp

4/13/2014, 7:30:46 AM

Confirmations

6,319,958

Mined by

⛏️ wAGz9gyZWgxBxAyVrKrWDzMw21kbo8NYQpw

Merkle Root

098e4e09beb085b16c51bb4e1fe398caee5edb8964285e7b0da868f7872788d5

Transactions (1)

Coinbase098e4e09beb085…a868f7872788d5

1 in → 20 out8.7800 XPM743 B

AGz9gyZW…bo8NYQpw AdFLJFhb…bsaVkAyh AMW1p9oT…2TzdaZxH AG9t8WDV…4bruShZ7 AbPcCMg4…719q6mAX

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.

1.988 × 10⁹⁷(98-digit number)

19884835781793509950…85634505540844377599

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

1.988 × 10⁹⁷(98-digit number)

19884835781793509950…85634505540844377599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.988 × 10⁹⁷(98-digit number)

19884835781793509950…85634505540844377601

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

3.976 × 10⁹⁷(98-digit number)

39769671563587019901…71269011081688755199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.976 × 10⁹⁷(98-digit number)

39769671563587019901…71269011081688755201

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

7.953 × 10⁹⁷(98-digit number)

79539343127174039802…42538022163377510399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.953 × 10⁹⁷(98-digit number)

79539343127174039802…42538022163377510401

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

1.590 × 10⁹⁸(99-digit number)

15907868625434807960…85076044326755020799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.590 × 10⁹⁸(99-digit number)

15907868625434807960…85076044326755020801

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

3.181 × 10⁹⁸(99-digit number)

31815737250869615921…70152088653510041599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.181 × 10⁹⁸(99-digit number)

31815737250869615921…70152088653510041601

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 #489,453

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