Block #87,920

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/29/2013, 6:10:06 AM · Difficulty 9.2719 · 6,720,238 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2558dfee06a71fef98f861d4c7059c72132479fd1cfdfda89b5c333028fd8764

View on Chainz ↗

Height

#87,920

Difficulty

9.271909

Transactions

Size

1.48 KB

Version

Bits

09459bda

Nonce

1,234,762

Timestamp

7/29/2013, 6:10:06 AM

Confirmations

6,720,238

Mined by

⛏️ P2SHAXaznK7J7syxThUrZ4Y2oajBHbPdWVvBVG

Merkle Root

e46700c58a7fb0159096ff0ecf1c5b821bb23388798b566c8c67afb5eb5a4e90

Transactions (4)

Coinbase9adfba0a2ed543…66782dffbae931

1 in → 1 out11.6500 XPM109 B

AXaznK7J…PdWVvBVG

059bbef1e90e4b…3a62e9cfc4e473

1 in → 1 out11.6200 XPM157 B

ANBV9EUK…YGogASJY

5b0038be4e8893…eb253ff7071f77

1 in → 2 out11.6100 XPM192 B

AVEJpYQq…AgHtQp2Z AJBd1os9…fQGeb8wa

dfdd195d8d1b77…ebe3c81188a203

6 in → 2 out0.1027 XPM968 B

AK3x8dvE…nYbmJccD AVdinSYA…dxAG2y7d

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.

1.157 × 10⁹²(93-digit number)

11579839041116142824…24737729792059609969

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

1.157 × 10⁹²(93-digit number)

11579839041116142824…24737729792059609969

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.157 × 10⁹²(93-digit number)

11579839041116142824…24737729792059609971

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

2.315 × 10⁹²(93-digit number)

23159678082232285649…49475459584119219939

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.315 × 10⁹²(93-digit number)

23159678082232285649…49475459584119219941

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

4.631 × 10⁹²(93-digit number)

46319356164464571298…98950919168238439879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.631 × 10⁹²(93-digit number)

46319356164464571298…98950919168238439881

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

9.263 × 10⁹²(93-digit number)

92638712328929142597…97901838336476879759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.263 × 10⁹²(93-digit number)

92638712328929142597…97901838336476879761

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

1.852 × 10⁹³(94-digit number)

18527742465785828519…95803676672953759519

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

Block #87,920

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