Block #857,246

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/17/2014, 4:59:52 PM · Difficulty 10.9676 · 5,976,390 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ae4784cc92c11ca37497b1c87216925420f87bb00f71a3294f757792825435a3

View on Chainz ↗

Height

#857,246

Difficulty

10.967556

Transactions

Size

1.08 KB

Version

Bits

0af7b1be

Nonce

144,166,507

Timestamp

12/17/2014, 4:59:52 PM

Confirmations

5,976,390

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

6d659a44450a9c59718ecb380b7685f161faacf402bbab0218abb9b0b3579a40

Transactions (5)

Coinbase5e59dc1c619342…cd01cf798ff533

1 in → 1 out8.3450 XPM116 B

ANSXnLY2…Sd25TjkD

5804e627f4d954…8dcc1e0d6b2bfb

1 in → 2 out8.2800 XPM225 B

AJdrcjFj…U2XAhkcx AHRoBSh4…BSVTQ36Q

f3c559b5afb280…938fcde7d596ae

1 in → 2 out8.2800 XPM225 B

AVZwze3C…1DNKwKx6 AXak1kLf…u9sbL2nG

512f26868dae19…b3741d2d245105

1 in → 2 out7.7656 XPM226 B

ATbchwJT…fQnohxM8 ALP6szJY…eEPSo5sX

b80dc93dc206e9…15becbb0a4c5d2

1 in → 2 out0.1138 XPM225 B

AJ8QzKXz…CZFYnFdS AcsgJALR…zciUucya

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.

5.012 × 10⁹⁷(98-digit number)

50123721767388027796…04591381405820887039

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

5.012 × 10⁹⁷(98-digit number)

50123721767388027796…04591381405820887039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.012 × 10⁹⁷(98-digit number)

50123721767388027796…04591381405820887041

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

1.002 × 10⁹⁸(99-digit number)

10024744353477605559…09182762811641774079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.002 × 10⁹⁸(99-digit number)

10024744353477605559…09182762811641774081

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

2.004 × 10⁹⁸(99-digit number)

20049488706955211118…18365525623283548159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.004 × 10⁹⁸(99-digit number)

20049488706955211118…18365525623283548161

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

4.009 × 10⁹⁸(99-digit number)

40098977413910422237…36731051246567096319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.009 × 10⁹⁸(99-digit number)

40098977413910422237…36731051246567096321

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

8.019 × 10⁹⁸(99-digit number)

80197954827820844474…73462102493134192639

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.019 × 10⁹⁸(99-digit number)

80197954827820844474…73462102493134192641

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 #857,246

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