Block #1,177,266

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 7/30/2015, 5:08:59 PM · Difficulty 10.9362 · 5,627,866 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

9b2780d927cab1fb92393b5aaba95b26fe901e87218354f1b083e4f6558a2f4b

View on Chainz ↗

Height

#1,177,266

Difficulty

10.936234

Transactions

Size

3.43 KB

Version

Bits

0aefad09

Nonce

1,471,708,946

Timestamp

7/30/2015, 5:08:59 PM

Confirmations

5,627,866

Mined by

⛏️ P2SHAaim4a5muT4bwBatY25qWuT9ruG3BHstK7

Merkle Root

b1bcbfc5c5f2a6eb7e3626d689ad13a04c9d549097cdc1f050cfe743a477111a

Transactions (3)

Coinbasee0275c4bd3390a…63f4fdaceb412d

1 in → 1 out8.3900 XPM110 B

Aaim4a5m…G3BHstK7

4a8ac2dfa3df92…a1844b9e5888bd

1 in → 37 out24.9800 XPM1.38 KB

AHkms3nt…nkSsZEE6 AZ7bdUiQ…VWjibCPn AGy4UsxS…kBDLvtSF AUAzdtai…sccBzNG7 AHuNyLCm…imZ3aTaL

99bb1c3531a7f8…a76928182966b3

1 in → 51 out18.3156 XPM1.85 KB

AcmhVcUJ…JLTQEtJS AbFWECxS…Zmp2qruU AbCcuXSu…yH8gpwqa AaXusZgQ…Q5ADHMTS ANLNkrvp…A8LrkHpm

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.

1.034 × 10⁹⁵(96-digit number)

10340593603722069224…64851212043192185599

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

1.034 × 10⁹⁵(96-digit number)

10340593603722069224…64851212043192185599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.034 × 10⁹⁵(96-digit number)

10340593603722069224…64851212043192185601

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

2.068 × 10⁹⁵(96-digit number)

20681187207444138448…29702424086384371199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.068 × 10⁹⁵(96-digit number)

20681187207444138448…29702424086384371201

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

4.136 × 10⁹⁵(96-digit number)

41362374414888276896…59404848172768742399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.136 × 10⁹⁵(96-digit number)

41362374414888276896…59404848172768742401

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

8.272 × 10⁹⁵(96-digit number)

82724748829776553792…18809696345537484799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.272 × 10⁹⁵(96-digit number)

82724748829776553792…18809696345537484801

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

1.654 × 10⁹⁶(97-digit number)

16544949765955310758…37619392691074969599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.654 × 10⁹⁶(97-digit number)

16544949765955310758…37619392691074969601

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