Block #668,177

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 8/8/2014, 2:05:55 AM · Difficulty 10.9634 · 6,142,094 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

99691a24e264c6f7e6e68b7f6273d4552f5fbf099cc6d8b9f70e3aa18e6b7aa2

View on Chainz ↗

Height

#668,177

Difficulty

10.963419

Transactions

Size

2.19 KB

Version

Bits

0af6a2a8

Nonce

1,255,780,533

Timestamp

8/8/2014, 2:05:55 AM

Confirmations

6,142,094

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

0b123eec393b987e356fd842b098d766e27b530c3bc68d5bfa451566e7b96bf5

Transactions (2)

Coinbasedbb1898883aaad…c8db8f3c999d44

1 in → 1 out8.3400 XPM116 B

ANSXnLY2…Sd25TjkD

dd82dc8e0af40a…795c032e748bfa

13 in → 3 out4.0221 XPM1.99 KB

AM6M7ug7…EArLB49G AeKNrjNj…1NEq95Ta AKc9Rmjx…Bir3N5mm

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.

3.069 × 10⁹⁵(96-digit number)

30696305358528033690…04838389713123314879

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

3.069 × 10⁹⁵(96-digit number)

30696305358528033690…04838389713123314879

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.069 × 10⁹⁵(96-digit number)

30696305358528033690…04838389713123314881

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

6.139 × 10⁹⁵(96-digit number)

61392610717056067381…09676779426246629759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.139 × 10⁹⁵(96-digit number)

61392610717056067381…09676779426246629761

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

1.227 × 10⁹⁶(97-digit number)

12278522143411213476…19353558852493259519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.227 × 10⁹⁶(97-digit number)

12278522143411213476…19353558852493259521

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

2.455 × 10⁹⁶(97-digit number)

24557044286822426952…38707117704986519039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.455 × 10⁹⁶(97-digit number)

24557044286822426952…38707117704986519041

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

4.911 × 10⁹⁶(97-digit number)

49114088573644853904…77414235409973038079

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.911 × 10⁹⁶(97-digit number)

49114088573644853904…77414235409973038081

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

9.822 × 10⁹⁶(97-digit number)

98228177147289707809…54828470819946076159

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 #668,177

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