Block #708,568

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 9/5/2014, 6:46:58 PM · Difficulty 10.9574 · 6,101,569 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c506b88dcdfb1cd717c7a3257c5adaa7755fd57b6a12c878e202c93985945dcc

View on Chainz ↗

Height

#708,568

Difficulty

10.957435

Transactions

Size

729 B

Version

Bits

0af51a7a

Nonce

611,881,987

Timestamp

9/5/2014, 6:46:58 PM

Confirmations

6,101,569

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

bef6f7ee5bc8644c6eb21bd02b9c54688143000c380423c9e05ed1b2aa61843f

Transactions (2)

Coinbase32cc32cdf1ecaa…401a377d101b64

1 in → 1 out8.3300 XPM116 B

ANSXnLY2…Sd25TjkD

b5f57a9e0a9644…a598944d2d543a

3 in → 2 out7.6228 XPM523 B

AWVW5xai…GbenxxLy ARV7ntob…QKAQxrtv

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.

3.161 × 10⁹⁵(96-digit number)

31617246951696643276…22011987258261507119

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

3.161 × 10⁹⁵(96-digit number)

31617246951696643276…22011987258261507119

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.161 × 10⁹⁵(96-digit number)

31617246951696643276…22011987258261507121

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

6.323 × 10⁹⁵(96-digit number)

63234493903393286553…44023974516523014239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.323 × 10⁹⁵(96-digit number)

63234493903393286553…44023974516523014241

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

1.264 × 10⁹⁶(97-digit number)

12646898780678657310…88047949033046028479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.264 × 10⁹⁶(97-digit number)

12646898780678657310…88047949033046028481

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

2.529 × 10⁹⁶(97-digit number)

25293797561357314621…76095898066092056959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.529 × 10⁹⁶(97-digit number)

25293797561357314621…76095898066092056961

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

5.058 × 10⁹⁶(97-digit number)

50587595122714629242…52191796132184113919

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.058 × 10⁹⁶(97-digit number)

50587595122714629242…52191796132184113921

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

1.011 × 10⁹⁷(98-digit number)

10117519024542925848…04383592264368227839

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 #708,568

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