Block #989,904

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/25/2015, 8:57:41 AM · Difficulty 10.8522 · 5,841,191 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

836a5284db602689d8f80af985324cf310403218e923b4fb567859af08489a7d

View on Chainz ↗

Height

#989,904

Difficulty

10.852203

Transactions

Size

425 B

Version

Bits

0ada2a00

Nonce

469,622,118

Timestamp

3/25/2015, 8:57:41 AM

Confirmations

5,841,191

Mined by

⛏️ P2SHAK5LCCgtP6tFSDGw9SzCjNCnVuPv8Sttre

Merkle Root

af6c81d56d251e16da156df92f072e2ae416f56451266142b62d079bc13999ba

Transactions (2)

Coinbase2b6f84a912a11e…c3353f1debf088

1 in → 1 out8.4950 XPM109 B

AK5LCCgt…Pv8Sttre

c076299ff132c9…e2cff5c20f1d27

1 in → 2 out0.1014 XPM227 B

AHeDxcSa…Z9RmkpT8 AYnkKHsB…WJssY4JR

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.

1.833 × 10⁹¹(92-digit number)

18332190218843605346…13216409536810197389

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

1.833 × 10⁹¹(92-digit number)

18332190218843605346…13216409536810197389

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.833 × 10⁹¹(92-digit number)

18332190218843605346…13216409536810197391

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

3.666 × 10⁹¹(92-digit number)

36664380437687210693…26432819073620394779

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.666 × 10⁹¹(92-digit number)

36664380437687210693…26432819073620394781

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

7.332 × 10⁹¹(92-digit number)

73328760875374421387…52865638147240789559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.332 × 10⁹¹(92-digit number)

73328760875374421387…52865638147240789561

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

1.466 × 10⁹²(93-digit number)

14665752175074884277…05731276294481579119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.466 × 10⁹²(93-digit number)

14665752175074884277…05731276294481579121

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

2.933 × 10⁹²(93-digit number)

29331504350149768555…11462552588963158239

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.933 × 10⁹²(93-digit number)

29331504350149768555…11462552588963158241

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 #989,904

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