Block #684,940

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 8/20/2014, 9:08:24 AM · Difficulty 10.9566 · 6,125,361 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

59c633dee2ee47162362c18212f89f1add65f3318cd44596069212c3e46f7362

View on Chainz ↗

Height

#684,940

Difficulty

10.956598

Transactions

Size

1.11 KB

Version

Bits

0af4e39b

Nonce

412,676,921

Timestamp

8/20/2014, 9:08:24 AM

Confirmations

6,125,361

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

a4eddfaa427eb101988da0140dca5d1dff213dfdbf8ddc0ed84aa6e9cc3edeb2

Transactions (3)

Coinbase1c39adc8733437…c0d96ee01fa036

1 in → 1 out8.3400 XPM116 B

ANSXnLY2…Sd25TjkD

f50269e06a13b7…2972b2053d901c

4 in → 3 out4.1576 XPM706 B

ARJQsNEx…UvYvuSPW AeKNrjNj…1NEq95Ta AYt5grtd…X2DHMmwW

7fe8a309a47bb7…f21df3f1a11d67

1 in → 2 out1.2877 XPM226 B

Abs1CTRR…uk6ieBYF AV1Vad2o…LLLkB4FU

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.

5.890 × 10⁹⁶(97-digit number)

58902552257680625275…78693618105098874559

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

5.890 × 10⁹⁶(97-digit number)

58902552257680625275…78693618105098874559

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.890 × 10⁹⁶(97-digit number)

58902552257680625275…78693618105098874561

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

1.178 × 10⁹⁷(98-digit number)

11780510451536125055…57387236210197749119

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.178 × 10⁹⁷(98-digit number)

11780510451536125055…57387236210197749121

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

2.356 × 10⁹⁷(98-digit number)

23561020903072250110…14774472420395498239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.356 × 10⁹⁷(98-digit number)

23561020903072250110…14774472420395498241

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

4.712 × 10⁹⁷(98-digit number)

47122041806144500220…29548944840790996479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.712 × 10⁹⁷(98-digit number)

47122041806144500220…29548944840790996481

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

9.424 × 10⁹⁷(98-digit number)

94244083612289000441…59097889681581992959

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.424 × 10⁹⁷(98-digit number)

94244083612289000441…59097889681581992961

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

1.884 × 10⁹⁸(99-digit number)

18848816722457800088…18195779363163985919

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 #684,940

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