Block #679,862

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 8/16/2014, 6:53:08 AM · Difficulty 10.9629 · 6,116,282 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e8e045c825fc611a1c32b183aececd3c4e23ca4034459d85e732902f62c34bca

View on Chainz ↗

Height

#679,862

Difficulty

10.962946

Transactions

Size

887 B

Version

Bits

0af6839b

Nonce

1,361,695,559

Timestamp

8/16/2014, 6:53:08 AM

Confirmations

6,116,282

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

8b941a851bd044115200302a5002301b7563614ee3c074bfb993152632126fa7

Transactions (4)

Coinbase0876ad9287e1e1…d234cdb54bbc21

1 in → 1 out8.3400 XPM116 B

ANSXnLY2…Sd25TjkD

f43a22a9b5f885…8d1f6d53462608

1 in → 2 out8.2900 XPM227 B

AXtGFfPj…UY8uHkHy Ad3heTyY…bABUKnfk

d7792062c91226…f5b0e4ad346074

1 in → 2 out8.2900 XPM226 B

Abs1CTRR…uk6ieBYF ATeF5wGR…q6trfmf5

b8091e54029ca5…14a6e30d976609

1 in → 2 out8.2900 XPM226 B

AS9ZCvju…bu3NEFwZ AU3JMuPZ…1N7K1DSw

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.

9.146 × 10⁹⁸(99-digit number)

91462264190577227453…84707207747260497919

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

9.146 × 10⁹⁸(99-digit number)

91462264190577227453…84707207747260497919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.146 × 10⁹⁸(99-digit number)

91462264190577227453…84707207747260497921

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

1.829 × 10⁹⁹(100-digit number)

18292452838115445490…69414415494520995839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.829 × 10⁹⁹(100-digit number)

18292452838115445490…69414415494520995841

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

3.658 × 10⁹⁹(100-digit number)

36584905676230890981…38828830989041991679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.658 × 10⁹⁹(100-digit number)

36584905676230890981…38828830989041991681

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

7.316 × 10⁹⁹(100-digit number)

73169811352461781962…77657661978083983359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.316 × 10⁹⁹(100-digit number)

73169811352461781962…77657661978083983361

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

1.463 × 10¹⁰⁰(101-digit number)

14633962270492356392…55315323956167966719

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.463 × 10¹⁰⁰(101-digit number)

14633962270492356392…55315323956167966721

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