Block #835,849

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/1/2014, 3:47:59 PM · Difficulty 10.9764 · 5,970,194 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6446a0a0e47f3a0fc959e6587b13f974f1caa8d453c7ea2f5d6aa643c02c7069

View on Chainz ↗

Height

#835,849

Difficulty

10.976369

Transactions

Size

1.80 KB

Version

Bits

0af9f356

Nonce

175,238,341

Timestamp

12/1/2014, 3:47:59 PM

Confirmations

5,970,194

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

73239fbecf94fac1f11d8eaf30babb5449bf96f564779c0ebe552be03f3430df

Transactions (3)

Coinbase61bad4cc0f078e…11d2455bbbaa1d

1 in → 1 out8.3200 XPM116 B

ANSXnLY2…Sd25TjkD

6976f0d1331c45…f7c663788f4133

8 in → 2 out62.9080 XPM1.23 KB

ASeN6Jze…JQfuJFhj AeFeMoxh…pRYx4Rma

c66feaeeed7b42…3fb51fb83396d4

2 in → 2 out2.0720 XPM375 B

AJgcJLsK…PmsdfHmT Ab6Fi1Xt…3cYbpTwA

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.

3.708 × 10⁹⁶(97-digit number)

37085967230433437075…17109416117691985919

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

3.708 × 10⁹⁶(97-digit number)

37085967230433437075…17109416117691985919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.708 × 10⁹⁶(97-digit number)

37085967230433437075…17109416117691985921

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

7.417 × 10⁹⁶(97-digit number)

74171934460866874150…34218832235383971839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.417 × 10⁹⁶(97-digit number)

74171934460866874150…34218832235383971841

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

1.483 × 10⁹⁷(98-digit number)

14834386892173374830…68437664470767943679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.483 × 10⁹⁷(98-digit number)

14834386892173374830…68437664470767943681

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

2.966 × 10⁹⁷(98-digit number)

29668773784346749660…36875328941535887359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.966 × 10⁹⁷(98-digit number)

29668773784346749660…36875328941535887361

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

5.933 × 10⁹⁷(98-digit number)

59337547568693499320…73750657883071774719

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.933 × 10⁹⁷(98-digit number)

59337547568693499320…73750657883071774721

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