Block #2,532,347

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/21/2018, 9:04:05 PM · Difficulty 10.9858 · 4,284,829 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e24861789062a72dd3100a523420f5b47077550d6f9d3e9bb08faf0b7d0acf3c

View on Chainz ↗

Height

#2,532,347

Difficulty

10.985792

Transactions

Size

461 B

Version

Bits

0afc5ce3

Nonce

143,563,308

Timestamp

2/21/2018, 9:04:05 PM

Confirmations

4,284,829

Mined by

⛏️ P2SHAdaj5kvr2hX9BfZnwhWfyj8CakT5Rxe7r6

Merkle Root

fb8558a5b8b9c62453adc65af69d74564664b5964d6bd2fbc6ce1f4f0a02111a

Transactions (2)

Coinbasef01528c90a83c8…05f1f7ae43f493

1 in → 1 out8.2800 XPM110 B

Adaj5kvr…T5Rxe7r6

129bb6b38ed5b9…4db79be16babc6

1 in → 3 out8.6843 XPM260 B

ARMxV9Cn…XS5q3JUu AHdcBgRC…QMQBUujf AKiRCe9z…xBZnc8JW

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.

8.745 × 10⁹⁶(97-digit number)

87452987148199255305…50853237252366131199

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

8.745 × 10⁹⁶(97-digit number)

87452987148199255305…50853237252366131199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.745 × 10⁹⁶(97-digit number)

87452987148199255305…50853237252366131201

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

1.749 × 10⁹⁷(98-digit number)

17490597429639851061…01706474504732262399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.749 × 10⁹⁷(98-digit number)

17490597429639851061…01706474504732262401

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

3.498 × 10⁹⁷(98-digit number)

34981194859279702122…03412949009464524799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.498 × 10⁹⁷(98-digit number)

34981194859279702122…03412949009464524801

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

6.996 × 10⁹⁷(98-digit number)

69962389718559404244…06825898018929049599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.996 × 10⁹⁷(98-digit number)

69962389718559404244…06825898018929049601

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

1.399 × 10⁹⁸(99-digit number)

13992477943711880848…13651796037858099199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.399 × 10⁹⁸(99-digit number)

13992477943711880848…13651796037858099201

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 #2,532,347

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