Block #298,637

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/7/2013, 11:14:33 AM · Difficulty 9.9920 · 6,519,366 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6d876d04a9b0072300f0b0e8dec166b7c8038c6657322b33a9e6ddf847e2d6c9

View on Chainz ↗

Height

#298,637

Difficulty

9.991970

Transactions

Size

1.11 KB

Version

Bits

09fdf1b8

Nonce

82,638

Timestamp

12/7/2013, 11:14:33 AM

Confirmations

6,519,366

Mined by

⛏️ aRAPeshfYVKJ2qg4aRhC5FMjPmxg3PKcKMKH

Merkle Root

c351422808c35fd96b63be9dcb6fa8a91a4e2cbc6b55f6918f6e4a6784a041e2

Transactions (1)

Coinbasec351422808c35f…6e4a6784a041e2

1 in → 29 out9.9800 XPM1.02 KB

APeshfYV…3PKcKMKH AQyr8Lw3…hs4nt3Pn AJzWx2VD…j4ZSMit5 Acs9SHrk…QJSB8SFG AMdvB6BS…DPq9FYdA

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.

7.140 × 10⁹⁰(91-digit number)

71408046551038843919…22913744355049135359

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

7.140 × 10⁹⁰(91-digit number)

71408046551038843919…22913744355049135359

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.140 × 10⁹⁰(91-digit number)

71408046551038843919…22913744355049135361

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

1.428 × 10⁹¹(92-digit number)

14281609310207768783…45827488710098270719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.428 × 10⁹¹(92-digit number)

14281609310207768783…45827488710098270721

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

2.856 × 10⁹¹(92-digit number)

28563218620415537567…91654977420196541439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.856 × 10⁹¹(92-digit number)

28563218620415537567…91654977420196541441

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

5.712 × 10⁹¹(92-digit number)

57126437240831075135…83309954840393082879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.712 × 10⁹¹(92-digit number)

57126437240831075135…83309954840393082881

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

1.142 × 10⁹²(93-digit number)

11425287448166215027…66619909680786165759

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.142 × 10⁹²(93-digit number)

11425287448166215027…66619909680786165761

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 #298,637

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