Block #856,735

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 12/17/2014, 7:29:42 AM · Difficulty 10.9679 · 5,954,369 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

0af94e1b0e2820ae6cf5f3fb80564ab28a347cb42ce2f7e43c667bb7906f794e

View on Chainz ↗

Height

#856,735

Difficulty

10.967922

Transactions

Size

1.22 KB

Version

Bits

0af7c9bf

Nonce

2,218,177,357

Timestamp

12/17/2014, 7:29:42 AM

Confirmations

5,954,369

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

16e3673d67fc7021b8a963ccc0aed2bcf00a20ee6a3123cbb6ea7b3e8a2c53e0

Transactions (4)

Coinbase48d5d93b865371…f5d960a7e135e2

1 in → 1 out8.3400 XPM116 B

ANSXnLY2…Sd25TjkD

99b2ee4a4fd9dd…3026b7ac5d8ade

3 in → 4 out3362.3066 XPM591 B

AMQnvq2u…CaND99NC AGf4bxML…tCqWcVMH ASrYeiHQ…GZsXQfSy AcAFW717…V1pWEX3J

57de4f38701c64…53e0aed194b25e

1 in → 2 out0.1183 XPM225 B

ARD9PV47…xATeb4Kh AGtPmw84…geMFCNKh

c18c9a782bbde4…3f8ab817a6a4f9

1 in → 2 out0.1183 XPM226 B

Ad4acZCe…8BbDgvZY ASiWqZEz…CkQkmtES

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.

1.111 × 10⁹⁶(97-digit number)

11118483484536300152…36978739727067381759

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

1.111 × 10⁹⁶(97-digit number)

11118483484536300152…36978739727067381759

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.111 × 10⁹⁶(97-digit number)

11118483484536300152…36978739727067381761

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

2.223 × 10⁹⁶(97-digit number)

22236966969072600304…73957479454134763519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.223 × 10⁹⁶(97-digit number)

22236966969072600304…73957479454134763521

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

4.447 × 10⁹⁶(97-digit number)

44473933938145200608…47914958908269527039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.447 × 10⁹⁶(97-digit number)

44473933938145200608…47914958908269527041

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

8.894 × 10⁹⁶(97-digit number)

88947867876290401216…95829917816539054079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.894 × 10⁹⁶(97-digit number)

88947867876290401216…95829917816539054081

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

1.778 × 10⁹⁷(98-digit number)

17789573575258080243…91659835633078108159

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.778 × 10⁹⁷(98-digit number)

17789573575258080243…91659835633078108161

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

3.557 × 10⁹⁷(98-digit number)

35579147150516160486…83319671266156216319

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 #856,735

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