Block #683,014

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 8/18/2014, 6:08:56 PM · Difficulty 10.9600 · 6,134,980 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d263b7e0ee84fbf26a452a14b310c8361b1d3df75a222815ce220ff7758873ec

View on Chainz ↗

Height

#683,014

Difficulty

10.959959

Transactions

Size

243 B

Version

Bits

0af5bfe2

Nonce

1,559,020,967

Timestamp

8/18/2014, 6:08:56 PM

Confirmations

6,134,980

Mined by

⛏️ P2SHATrzKxLEMcqj8iissCT2aSSgyrdnfypiwk

Merkle Root

371678237de87eccd7e3278997e514853c92c7023c8019682720dca5e12979fd

Transactions (1)

Coinbase371678237de87e…20dca5e12979fd

1 in → 2 out8.3100 XPM152 B

ATrzKxLE…dnfypiwk ALPu3s2c…EJXLjVFh

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.

1.347 × 10⁹⁶(97-digit number)

13473336871716010493…06535113554460399999

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

1.347 × 10⁹⁶(97-digit number)

13473336871716010493…06535113554460399999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.347 × 10⁹⁶(97-digit number)

13473336871716010493…06535113554460400001

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

2.694 × 10⁹⁶(97-digit number)

26946673743432020987…13070227108920799999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.694 × 10⁹⁶(97-digit number)

26946673743432020987…13070227108920800001

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

5.389 × 10⁹⁶(97-digit number)

53893347486864041975…26140454217841599999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.389 × 10⁹⁶(97-digit number)

53893347486864041975…26140454217841600001

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

1.077 × 10⁹⁷(98-digit number)

10778669497372808395…52280908435683199999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.077 × 10⁹⁷(98-digit number)

10778669497372808395…52280908435683200001

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

2.155 × 10⁹⁷(98-digit number)

21557338994745616790…04561816871366399999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.155 × 10⁹⁷(98-digit number)

21557338994745616790…04561816871366400001

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

Block #683,014

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