Block #842,706

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/6/2014, 8:20:09 PM · Difficulty 10.9735 · 6,002,466 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

84683df2d2d3ec2290b0a4e92d47e386e3f4ce973d3842f455f4c6f24264c6c5

View on Chainz ↗

Height

#842,706

Difficulty

10.973517

Transactions

Size

800 B

Version

Bits

0af93863

Nonce

542,032,459

Timestamp

12/6/2014, 8:20:09 PM

Confirmations

6,002,466

Mined by

⛏️ P2SHAJWywPhj1TZL6D488ZX3gyHbfC9ahPX7Xg

Merkle Root

74a9a23b8edc78ff4ff6843147a49797372db49d14d9f19cda1fd91f3a432981

Transactions (3)

Coinbaseeb5690dbf0c0d7…9acea31351c737

1 in → 1 out8.3100 XPM110 B

AJWywPhj…9ahPX7Xg

9b8c3426798eda…3a10d3a0336a30

2 in → 2 out10.2396 XPM373 B

AWAbb2pL…4Wmht5QK ALXAy4W2…yNVtgSpX

a23522d02464b9…349e861cdd68d5

1 in → 2 out6.5132 XPM226 B

AMTvqX3a…sxpwNFyf AJjwgzTF…gXxjRrcL

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.

1.323 × 10⁹⁶(97-digit number)

13236276610879684072…25256668245781542399

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

1.323 × 10⁹⁶(97-digit number)

13236276610879684072…25256668245781542399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.323 × 10⁹⁶(97-digit number)

13236276610879684072…25256668245781542401

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

2.647 × 10⁹⁶(97-digit number)

26472553221759368145…50513336491563084799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.647 × 10⁹⁶(97-digit number)

26472553221759368145…50513336491563084801

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

5.294 × 10⁹⁶(97-digit number)

52945106443518736291…01026672983126169599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.294 × 10⁹⁶(97-digit number)

52945106443518736291…01026672983126169601

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

1.058 × 10⁹⁷(98-digit number)

10589021288703747258…02053345966252339199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.058 × 10⁹⁷(98-digit number)

10589021288703747258…02053345966252339201

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

2.117 × 10⁹⁷(98-digit number)

21178042577407494516…04106691932504678399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.117 × 10⁹⁷(98-digit number)

21178042577407494516…04106691932504678401

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 #842,706

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