Block #683,424

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 8/19/2014, 2:31:39 AM · Difficulty 10.9592 · 6,131,429 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

80c5023519a296e301ee389172ccbf73c3d0d6c4afa0ac7d9e2c53690bd6987e

View on Chainz ↗

Height

#683,424

Difficulty

10.959221

Transactions

Size

243 B

Version

Bits

0af58f7d

Nonce

597,707,519

Timestamp

8/19/2014, 2:31:39 AM

Confirmations

6,131,429

Mined by

⛏️ P2SHATrzKxLEMcqj8iissCT2aSSgyrdnfypiwk

Merkle Root

91859285d7b5c0e4cf71e7a0baf987a64a4e338ce0b8188424c23e79ccaaab87

Transactions (1)

Coinbase91859285d7b5c0…c23e79ccaaab87

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.

2.226 × 10⁹⁶(97-digit number)

22265078174166026569…32813585767804518399

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

2.226 × 10⁹⁶(97-digit number)

22265078174166026569…32813585767804518399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.226 × 10⁹⁶(97-digit number)

22265078174166026569…32813585767804518401

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

4.453 × 10⁹⁶(97-digit number)

44530156348332053139…65627171535609036799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.453 × 10⁹⁶(97-digit number)

44530156348332053139…65627171535609036801

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

8.906 × 10⁹⁶(97-digit number)

89060312696664106278…31254343071218073599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.906 × 10⁹⁶(97-digit number)

89060312696664106278…31254343071218073601

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

1.781 × 10⁹⁷(98-digit number)

17812062539332821255…62508686142436147199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.781 × 10⁹⁷(98-digit number)

17812062539332821255…62508686142436147201

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

3.562 × 10⁹⁷(98-digit number)

35624125078665642511…25017372284872294399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.562 × 10⁹⁷(98-digit number)

35624125078665642511…25017372284872294401

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

7.124 × 10⁹⁷(98-digit number)

71248250157331285022…50034744569744588799

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 #683,424

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