Block #89,880

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/30/2013, 4:43:32 PM · Difficulty 9.2554 · 6,715,226 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e42cc416a1176723e7bdc833de56997e081a0a2206b5de40623acb7643a9c49e

View on Chainz ↗

Height

#89,880

Difficulty

9.255408

Transactions

Size

5.88 KB

Version

Bits

0941626e

Nonce

24,049

Timestamp

7/30/2013, 4:43:32 PM

Confirmations

6,715,226

Mined by

⛏️ P2SHASxoQANX3YeXsFgL4F2AmVuJHzm3maWw23

Merkle Root

b2f633150bfb56869bd3459db4e3455caa922f9472aa312b0fd50bd7f267bc6a

Transactions (4)

Coinbase5bc99ab0c1c70c…d1b1785efb7511

1 in → 1 out11.7300 XPM109 B

ASxoQANX…m3maWw23

544d9455f73862…e65c2c0cca196e

9 in → 1 out154.1100 XPM1.27 KB

AMcc2mYT…JHXGJfcZ

ff6f83e18da96c…486dea5522ddbb

33 in → 2 out377.9500 XPM3.78 KB

AT2YZ4xE…GP2uhoY5 AGfz3APU…kNJNtgfb

2e64fb9e73c8cc…0c6f0c18a53014

4 in → 1 out1.0000 XPM637 B

AGfz3APU…kNJNtgfb

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.

9.172 × 10¹¹²(113-digit number)

91726639384207651203…67787852602476192249

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

9.172 × 10¹¹²(113-digit number)

91726639384207651203…67787852602476192249

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.172 × 10¹¹²(113-digit number)

91726639384207651203…67787852602476192251

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

1.834 × 10¹¹³(114-digit number)

18345327876841530240…35575705204952384499

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.834 × 10¹¹³(114-digit number)

18345327876841530240…35575705204952384501

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

3.669 × 10¹¹³(114-digit number)

36690655753683060481…71151410409904768999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.669 × 10¹¹³(114-digit number)

36690655753683060481…71151410409904769001

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

7.338 × 10¹¹³(114-digit number)

73381311507366120962…42302820819809537999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.338 × 10¹¹³(114-digit number)

73381311507366120962…42302820819809538001

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

1.467 × 10¹¹⁴(115-digit number)

14676262301473224192…84605641639619075999

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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