Block #1,099,135

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 6/10/2015, 10:56:33 PM · Difficulty 10.7615 · 5,715,917 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

5e3d156b807ee4ac263b358bfae8fef9d25f02dd4e738655f57832529e31d8f0

View on Chainz ↗

Height

#1,099,135

Difficulty

10.761481

Transactions

Size

3.52 KB

Version

Bits

0ac2f06d

Nonce

411,774,493

Timestamp

6/10/2015, 10:56:33 PM

Confirmations

5,715,917

Mined by

⛏️ P2SHAJCEY9yyy2DERzsA24UUtHTMGPtg97E6zm

Merkle Root

6c3ac1f4e6326ea25b5716526c7184c07eb908d275a1348af618b460ca34d409

Transactions (3)

Coinbase863726e56e4a88…a01f207570cf34

1 in → 1 out8.6600 XPM116 B

AJCEY9yy…tg97E6zm

c8befe07f42e14…73a0bb35e6455d

1 in → 51 out65.2131 XPM1.85 KB

AcAYXubV…72sadqng AbSwxqk6…2UN15uc1 AGrojGJ2…agp341GG AejcsRHy…X15pK4mH ATkiCeum…91r8eHmY

d929b8d3a87613…c1c728c565d195

3 in → 31 out0.5521 XPM1.47 KB

ANneNqro…1Yc6UxGE AdjvfFrG…fzzZ2ufk AGdCDPCJ…wvuFRxN7 ARnkUT2V…sj7UhYpb AWTSKqr7…JPPcfURC

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.

9.968 × 10⁹⁷(98-digit number)

99682142833855358580…68826518710150041599

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

9.968 × 10⁹⁷(98-digit number)

99682142833855358580…68826518710150041599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.968 × 10⁹⁷(98-digit number)

99682142833855358580…68826518710150041601

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

1.993 × 10⁹⁸(99-digit number)

19936428566771071716…37653037420300083199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.993 × 10⁹⁸(99-digit number)

19936428566771071716…37653037420300083201

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

3.987 × 10⁹⁸(99-digit number)

39872857133542143432…75306074840600166399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.987 × 10⁹⁸(99-digit number)

39872857133542143432…75306074840600166401

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

7.974 × 10⁹⁸(99-digit number)

79745714267084286864…50612149681200332799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.974 × 10⁹⁸(99-digit number)

79745714267084286864…50612149681200332801

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

1.594 × 10⁹⁹(100-digit number)

15949142853416857372…01224299362400665599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.594 × 10⁹⁹(100-digit number)

15949142853416857372…01224299362400665601

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 #1,099,135

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