Block #859,449

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/19/2014, 11:40:06 AM · Difficulty 10.9653 · 5,966,164 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b8e2b35be3376607c52911c66cf0765d06a419eed3c57ff10c5c24df3897f006

View on Chainz ↗

Height

#859,449

Difficulty

10.965278

Transactions

Size

2.74 KB

Version

Bits

0af71c76

Nonce

959,224,669

Timestamp

12/19/2014, 11:40:06 AM

Confirmations

5,966,164

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

f72d4861c25f4ee7d7524f97445c68fa6280eb1028371907ee93b44ef049648a

Transactions (4)

Coinbase323632ccbe7966…ff61eb2756361c

1 in → 1 out8.3500 XPM116 B

ANSXnLY2…Sd25TjkD

25fdb9a320c070…a2ecc8b565509d

1 in → 2 out4.3350 XPM226 B

AeudUKcq…YRjuNnT3 AHQ8J1zz…R9naRtck

5c1e07bc9123d2…e7c665b8171dff

1 in → 2 out4.3300 XPM227 B

AW7CUBwN…Dk5qJ7rW AJHWTJCa…oLXM6WuA

3b81f414ba611f…cd068c09e5b002

14 in → 2 out4.0106 XPM2.10 KB

AGxLoYai…mFPZwsG8 ASYq6deE…EKNcimUt

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.

6.559 × 10⁹⁴(95-digit number)

65599818638204155374…46176945936993290619

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

6.559 × 10⁹⁴(95-digit number)

65599818638204155374…46176945936993290619

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.559 × 10⁹⁴(95-digit number)

65599818638204155374…46176945936993290621

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

1.311 × 10⁹⁵(96-digit number)

13119963727640831074…92353891873986581239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.311 × 10⁹⁵(96-digit number)

13119963727640831074…92353891873986581241

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

2.623 × 10⁹⁵(96-digit number)

26239927455281662149…84707783747973162479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.623 × 10⁹⁵(96-digit number)

26239927455281662149…84707783747973162481

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

5.247 × 10⁹⁵(96-digit number)

52479854910563324299…69415567495946324959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.247 × 10⁹⁵(96-digit number)

52479854910563324299…69415567495946324961

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

1.049 × 10⁹⁶(97-digit number)

10495970982112664859…38831134991892649919

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.049 × 10⁹⁶(97-digit number)

10495970982112664859…38831134991892649921

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 #859,449

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