Block #857,179

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 12/17/2014, 3:42:29 PM · Difficulty 10.9676 · 5,985,134 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

01685941b96b28a5c013c31b4d10888adbf636bf4a66e2e0b218355fbe0a1c6e

View on Chainz ↗

Height

#857,179

Difficulty

10.967635

Transactions

Size

877 B

Version

Bits

0af7b6ea

Nonce

680,063,407

Timestamp

12/17/2014, 3:42:29 PM

Confirmations

5,985,134

Mined by

⛏️ P2SHAU3iPtH3k5FuM5H9ruN1AhiQoXt25Lg2BP

Merkle Root

f98820b04c542da98f899c7f0775a4e7db2a6c2fb33cf750e7dc7ee7a3faa94a

Transactions (4)

Coinbasecc043fdd0af87c…25e07a9181ce11

1 in → 1 out8.3400 XPM109 B

AU3iPtH3…t25Lg2BP

37c7033fda2b9b…1f6a0482461618

1 in → 2 out4.9610 XPM226 B

ASLVM69h…wGmcCXhM ALP6szJY…eEPSo5sX

046315f0138249…58c0fa66299b3c

1 in → 2 out0.4330 XPM225 B

ALzumW44…GSmhc6y8 AafjkAm7…hdWm53PA

c15a9d87692d6f…3ce5687dc53497

1 in → 2 out0.7224 XPM226 B

ALrjikNV…zfVrwqqu AMZdQRhu…FdFXXaVp

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.

1.565 × 10⁹⁶(97-digit number)

15652353002958711402…52244158817303993599

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

1.565 × 10⁹⁶(97-digit number)

15652353002958711402…52244158817303993599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.565 × 10⁹⁶(97-digit number)

15652353002958711402…52244158817303993601

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

3.130 × 10⁹⁶(97-digit number)

31304706005917422805…04488317634607987199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.130 × 10⁹⁶(97-digit number)

31304706005917422805…04488317634607987201

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

6.260 × 10⁹⁶(97-digit number)

62609412011834845610…08976635269215974399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.260 × 10⁹⁶(97-digit number)

62609412011834845610…08976635269215974401

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

1.252 × 10⁹⁷(98-digit number)

12521882402366969122…17953270538431948799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.252 × 10⁹⁷(98-digit number)

12521882402366969122…17953270538431948801

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

2.504 × 10⁹⁷(98-digit number)

25043764804733938244…35906541076863897599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.504 × 10⁹⁷(98-digit number)

25043764804733938244…35906541076863897601

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

5.008 × 10⁹⁷(98-digit number)

50087529609467876488…71813082153727795199

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 #857,179

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