Block #1,182,686

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 8/4/2015, 4:14:03 PM · Difficulty 10.9104 · 5,634,117 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

0162b7cdbf22f88b52f0540d194bef6d87c33eca4132ede12b2d4ba926aa0b5b

View on Chainz ↗

Height

#1,182,686

Difficulty

10.910395

Transactions

Size

3.77 KB

Version

Bits

0ae90fa5

Nonce

626,888,013

Timestamp

8/4/2015, 4:14:03 PM

Confirmations

5,634,117

Mined by

⛏️ P2SHAJCEY9yyy2DERzsA24UUtHTMGPtg97E6zm

Merkle Root

8c8a01907fb522704429739378aade0735ef8120c6e6c3daae5cc9d449d6f5e0

Transactions (3)

Coinbase06acc70d542a30…4df72fb513e4f1

1 in → 1 out8.4400 XPM116 B

AJCEY9yy…tg97E6zm

d796a17fde0e84…9fbe7941215bde

1 in → 47 out22.6937 XPM1.71 KB

AH2bh7Yt…WVoovT9G APehMwW1…WuXqBKVQ ATPX2tFW…rvDACefF AZcvXaEC…gstDfNmL AaDRErhi…Bqi9eMAG

6341683bf78509…174b2af792a5fd

1 in → 51 out11.6125 XPM1.85 KB

AaR2V7mf…5pES65VG ATkiCeum…91r8eHmY AJab5pQJ…NDncq51r AL23rBzY…6jZqyH2W AeQBW1K2…fUM128CE

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.

6.578 × 10⁹⁷(98-digit number)

65781432735086553505…80273084537087231999

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

6.578 × 10⁹⁷(98-digit number)

65781432735086553505…80273084537087231999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.578 × 10⁹⁷(98-digit number)

65781432735086553505…80273084537087232001

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

1.315 × 10⁹⁸(99-digit number)

13156286547017310701…60546169074174463999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.315 × 10⁹⁸(99-digit number)

13156286547017310701…60546169074174464001

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

2.631 × 10⁹⁸(99-digit number)

26312573094034621402…21092338148348927999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.631 × 10⁹⁸(99-digit number)

26312573094034621402…21092338148348928001

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

5.262 × 10⁹⁸(99-digit number)

52625146188069242804…42184676296697855999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.262 × 10⁹⁸(99-digit number)

52625146188069242804…42184676296697856001

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

1.052 × 10⁹⁹(100-digit number)

10525029237613848560…84369352593395711999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.052 × 10⁹⁹(100-digit number)

10525029237613848560…84369352593395712001

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 #1,182,686

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