Block #857,969

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 12/18/2014, 5:58:31 AM · Difficulty 10.9672 · 5,984,331 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

83436fd0faf4edb8799cfe1a2a806cc40575d61cc10511dd871abc3de9826cae

View on Chainz ↗

Height

#857,969

Difficulty

10.967220

Transactions

Size

1.08 KB

Version

Bits

0af79bb9

Nonce

842,753,398

Timestamp

12/18/2014, 5:58:31 AM

Confirmations

5,984,331

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

043d70a93e45d8fa5feeff6bcee7ad4c947f955aa52178be254fd5246f066626

Transactions (5)

Coinbase106fa35bf37633…19f003ebe568b8

1 in → 1 out8.3550 XPM116 B

ANSXnLY2…Sd25TjkD

624b47aefecbeb…a497210f1595d3

1 in → 2 out4.3878 XPM227 B

ATfpj2u1…rN9HqLTG AV17UV4f…R9dzjh8a

06c54f4efbcfab…d1b888b4038e2d

1 in → 2 out0.0811 XPM225 B

AQmVTuw3…qvcaum7k AGeo25s3…ofVx18Uz

eed41170fc87db…380809286b6773

1 in → 2 out0.0808 XPM226 B

ASuvyh9J…7WBAomNw AMddmMyc…si77ypGa

54fe3a3193ce48…cbd98aab7fcc1c

1 in → 2 out0.0244 XPM226 B

ARPVchgq…YtjpkDa1 AHnvxEMm…fAuqMECg

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.

1.232 × 10⁹⁷(98-digit number)

12326573778422291792…30526979019811635199

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

1.232 × 10⁹⁷(98-digit number)

12326573778422291792…30526979019811635199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.232 × 10⁹⁷(98-digit number)

12326573778422291792…30526979019811635201

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

2.465 × 10⁹⁷(98-digit number)

24653147556844583585…61053958039623270399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.465 × 10⁹⁷(98-digit number)

24653147556844583585…61053958039623270401

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

4.930 × 10⁹⁷(98-digit number)

49306295113689167170…22107916079246540799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.930 × 10⁹⁷(98-digit number)

49306295113689167170…22107916079246540801

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

9.861 × 10⁹⁷(98-digit number)

98612590227378334340…44215832158493081599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.861 × 10⁹⁷(98-digit number)

98612590227378334340…44215832158493081601

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

1.972 × 10⁹⁸(99-digit number)

19722518045475666868…88431664316986163199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.972 × 10⁹⁸(99-digit number)

19722518045475666868…88431664316986163201

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

3.944 × 10⁹⁸(99-digit number)

39445036090951333736…76863328633972326399

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 #857,969

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