Block #186,661

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 9/30/2013, 1:06:50 AM · Difficulty 9.8669 · 6,607,802 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

fba8ab88a0bdaf706a107aa6573009ac4b10d2487f996771d903441011265c3a

View on Chainz ↗

Height

#186,661

Difficulty

9.866926

Transactions

Size

723 B

Version

Bits

09ddeee3

Nonce

53,870

Timestamp

9/30/2013, 1:06:50 AM

Confirmations

6,607,802

Mined by

⛏️ P2SHAbG35cX5itvDNCAvudaksKVXLV1ggEFgjQ

Merkle Root

aae845949176e843012c15c1255e3f2a3cf27f1696562940852826d92f8e52f3

Transactions (2)

Coinbase1d61bf31156b11…42c9ca431b6840

1 in → 1 out10.2700 XPM109 B

AbG35cX5…1ggEFgjQ

eda6c5c9918078…bba041d7aa1566

3 in → 2 out12.7032 XPM522 B

APfW95YS…HnHu1zGG Achmusid…dSSMpK8W

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.

2.590 × 10¹⁰⁰(101-digit number)

25901173677800118442…90686613997930719999

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

2.590 × 10¹⁰⁰(101-digit number)

25901173677800118442…90686613997930719999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.590 × 10¹⁰⁰(101-digit number)

25901173677800118442…90686613997930720001

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

5.180 × 10¹⁰⁰(101-digit number)

51802347355600236884…81373227995861439999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.180 × 10¹⁰⁰(101-digit number)

51802347355600236884…81373227995861440001

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

1.036 × 10¹⁰¹(102-digit number)

10360469471120047376…62746455991722879999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.036 × 10¹⁰¹(102-digit number)

10360469471120047376…62746455991722880001

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

2.072 × 10¹⁰¹(102-digit number)

20720938942240094753…25492911983445759999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.072 × 10¹⁰¹(102-digit number)

20720938942240094753…25492911983445760001

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

4.144 × 10¹⁰¹(102-digit number)

41441877884480189507…50985823966891519999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.144 × 10¹⁰¹(102-digit number)

41441877884480189507…50985823966891520001

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