Block #1,115,726

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 6/18/2015, 1:21:07 PM · Difficulty 10.9225 · 5,698,584 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

87fad3d0e7d716ce55162d6b4e2f258936d8994f552999a04699b5e5f87bc52e

View on Chainz ↗

Height

#1,115,726

Difficulty

10.922473

Transactions

Size

3.90 KB

Version

Bits

0aec272a

Nonce

610,119,052

Timestamp

6/18/2015, 1:21:07 PM

Confirmations

5,698,584

Mined by

⛏️ P2SHAJCEY9yyy2DERzsA24UUtHTMGPtg97E6zm

Merkle Root

dc2f303f0302e70692b057c67177ca14968d5e07998ac14117577f85a9d09a03

Transactions (3)

Coinbase25d193eaa0a57b…c8ae4f4bc60868

1 in → 1 out8.4100 XPM116 B

AJCEY9yy…tg97E6zm

de9fdabc827ef3…d0a07801e53375

1 in → 51 out55.3954 XPM1.85 KB

AU4f4km9…u8UnNcJ8 ATkiCeum…91r8eHmY ALmXRsLp…9xHwMMPt AbCcuXSu…yH8gpwqa AXyoDB3P…gVR3fWfe

2222a3510ab960…4f259da6d57f5c

1 in → 51 out2.6079 XPM1.85 KB

Ads4oV2s…6HF5N4ts AXMB5gUx…4GAc9wPZ ALynJXCh…mKKAQdNw ARjkNANT…Sqwc2PGr Ad1VoraV…Bn7uxPvx

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.

6.651 × 10⁹⁸(99-digit number)

66517248708248929846…87149914077562101759

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

6.651 × 10⁹⁸(99-digit number)

66517248708248929846…87149914077562101759

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.651 × 10⁹⁸(99-digit number)

66517248708248929846…87149914077562101761

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

1.330 × 10⁹⁹(100-digit number)

13303449741649785969…74299828155124203519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.330 × 10⁹⁹(100-digit number)

13303449741649785969…74299828155124203521

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

2.660 × 10⁹⁹(100-digit number)

26606899483299571938…48599656310248407039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.660 × 10⁹⁹(100-digit number)

26606899483299571938…48599656310248407041

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

5.321 × 10⁹⁹(100-digit number)

53213798966599143877…97199312620496814079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.321 × 10⁹⁹(100-digit number)

53213798966599143877…97199312620496814081

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

1.064 × 10¹⁰⁰(101-digit number)

10642759793319828775…94398625240993628159

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.064 × 10¹⁰⁰(101-digit number)

10642759793319828775…94398625240993628161

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 #1,115,726

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