Block #678,638

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 8/15/2014, 8:43:13 AM · Difficulty 10.9637 · 6,135,837 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a8ea86ffa5e62f03263d2efd73f4ac0eb129fbd2fdb06f40d5eacdda81238e5f

View on Chainz ↗

Height

#678,638

Difficulty

10.963679

Transactions

Size

1.08 KB

Version

Bits

0af6b3a3

Nonce

422,270,345

Timestamp

8/15/2014, 8:43:13 AM

Confirmations

6,135,837

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

ab50dd7475269edae0b98a6013e525d68bacab84d9f9b64346dc0f77f80db30c

Transactions (3)

Coinbase5c19e94bcecaf2…8d4349593ea7dc

1 in → 1 out8.3300 XPM116 B

ANSXnLY2…Sd25TjkD

89317d6e730346…646366cc9ac62c

4 in → 2 out10.2420 XPM670 B

AL9X5fHH…GGzCc6BL AQTxGdDq…jQGA3kti

30b63569ed9076…036710f253288c

1 in → 2 out1.9412 XPM226 B

AGMcnYSE…2nMYsP4y AWbYt63i…H2mAW2Wz

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.

6.150 × 10⁹⁵(96-digit number)

61500026087033788140…56876777998334127999

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

6.150 × 10⁹⁵(96-digit number)

61500026087033788140…56876777998334127999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.150 × 10⁹⁵(96-digit number)

61500026087033788140…56876777998334128001

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

1.230 × 10⁹⁶(97-digit number)

12300005217406757628…13753555996668255999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.230 × 10⁹⁶(97-digit number)

12300005217406757628…13753555996668256001

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

2.460 × 10⁹⁶(97-digit number)

24600010434813515256…27507111993336511999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.460 × 10⁹⁶(97-digit number)

24600010434813515256…27507111993336512001

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

4.920 × 10⁹⁶(97-digit number)

49200020869627030512…55014223986673023999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.920 × 10⁹⁶(97-digit number)

49200020869627030512…55014223986673024001

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

9.840 × 10⁹⁶(97-digit number)

98400041739254061025…10028447973346047999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.840 × 10⁹⁶(97-digit number)

98400041739254061025…10028447973346048001

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

1.968 × 10⁹⁷(98-digit number)

19680008347850812205…20056895946692095999

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 #678,638

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