Block #856,340

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 12/17/2014, 12:27:48 AM · Difficulty 10.9681 · 5,957,563 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ae76ecc5e88ddef14ba871e9b1868e1526cb66660481a4cbd56a985207e39c31

View on Chainz ↗

Height

#856,340

Difficulty

10.968090

Transactions

Size

1.23 KB

Version

Bits

0af7d4b9

Nonce

1,325,533,068

Timestamp

12/17/2014, 12:27:48 AM

Confirmations

5,957,563

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

ff447fd20f5ba8014f1ae538b296feaad503a3414d03ebf8b42e9093a859f155

Transactions (5)

Coinbase74b90cef6e0b59…331a9dc00b9da0

1 in → 1 out8.3500 XPM116 B

ANSXnLY2…Sd25TjkD

f1865ae4e6c543…c5ff986f110d78

1 in → 2 out8.2800 XPM226 B

AMTvqX3a…sxpwNFyf AaFprDWo…W7n3ow1a

6637aea442f9c9…b0894c39b24b34

2 in → 2 out0.6464 XPM376 B

AMoJsji6…a13Bp22Q AawtSJFu…BYwkV6F7

6818cf54c3af8a…cd456eeb9a1b05

1 in → 2 out0.0386 XPM225 B

ARfHHLu8…QfV9ZWQw APK1Rqki…kDhZERoe

76a6437733018b…26f6c5704af958

1 in → 2 out0.0363 XPM226 B

AbceonCh…QAPpQ5Td ATjSWzbe…BwCzQu5z

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.

7.723 × 10⁹⁷(98-digit number)

77233109355043359786…16749098045931525119

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

7.723 × 10⁹⁷(98-digit number)

77233109355043359786…16749098045931525119

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.723 × 10⁹⁷(98-digit number)

77233109355043359786…16749098045931525121

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

1.544 × 10⁹⁸(99-digit number)

15446621871008671957…33498196091863050239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.544 × 10⁹⁸(99-digit number)

15446621871008671957…33498196091863050241

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

3.089 × 10⁹⁸(99-digit number)

30893243742017343914…66996392183726100479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.089 × 10⁹⁸(99-digit number)

30893243742017343914…66996392183726100481

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

6.178 × 10⁹⁸(99-digit number)

61786487484034687828…33992784367452200959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.178 × 10⁹⁸(99-digit number)

61786487484034687828…33992784367452200961

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

1.235 × 10⁹⁹(100-digit number)

12357297496806937565…67985568734904401919

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.235 × 10⁹⁹(100-digit number)

12357297496806937565…67985568734904401921

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

2.471 × 10⁹⁹(100-digit number)

24714594993613875131…35971137469808803839

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 #856,340

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