Block #888,039

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 1/9/2015, 6:10:26 AM · Difficulty 10.9559 · 5,937,365 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8ad95a9c5c0333548b076d092b5c24e08d834f82bf9d67df293f3ffa50ec207a

View on Chainz ↗

Height

#888,039

Difficulty

10.955872

Transactions

Size

3.46 KB

Version

Bits

0af4b400

Nonce

12,665,612

Timestamp

1/9/2015, 6:10:26 AM

Confirmations

5,937,365

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

7715bfe38c9ecf4cfebc096307c678ef55511ab1d8d9e140a32187491d3b22d8

Transactions (2)

Coinbase977ccfc13f8fcd…05b80e34be7a0b

1 in → 1 out8.3800 XPM116 B

ANSXnLY2…Sd25TjkD

3a153800ce9089…d1c0c75fbfba83

22 in → 2 out500.0100 XPM3.25 KB

ANxSgqms…bVsZWYU2 AJjnK9uC…VreFquR4

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.

7.015 × 10⁹⁶(97-digit number)

70151195943674833492…10820307108913315839

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

7.015 × 10⁹⁶(97-digit number)

70151195943674833492…10820307108913315839

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.015 × 10⁹⁶(97-digit number)

70151195943674833492…10820307108913315841

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

1.403 × 10⁹⁷(98-digit number)

14030239188734966698…21640614217826631679

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.403 × 10⁹⁷(98-digit number)

14030239188734966698…21640614217826631681

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

2.806 × 10⁹⁷(98-digit number)

28060478377469933397…43281228435653263359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.806 × 10⁹⁷(98-digit number)

28060478377469933397…43281228435653263361

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

5.612 × 10⁹⁷(98-digit number)

56120956754939866794…86562456871306526719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.612 × 10⁹⁷(98-digit number)

56120956754939866794…86562456871306526721

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

1.122 × 10⁹⁸(99-digit number)

11224191350987973358…73124913742613053439

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.122 × 10⁹⁸(99-digit number)

11224191350987973358…73124913742613053441

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

2.244 × 10⁹⁸(99-digit number)

22448382701975946717…46249827485226106879

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 #888,039

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