Block #853,766

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/15/2014, 3:18:24 AM · Difficulty 10.9688 · 5,956,181 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

db8de8c51ffba72af6f335006aab73c85a2c84fe757c1554f0e1080a4f091102

View on Chainz ↗

Height

#853,766

Difficulty

10.968848

Transactions

Size

1.05 KB

Version

Bits

0af8066a

Nonce

55,637,502

Timestamp

12/15/2014, 3:18:24 AM

Confirmations

5,956,181

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

28e8e0b53ea911b5f51da4410f94c898898eb28a00832f77e593328f8fc23d04

Transactions (5)

Coinbaseda2d6d80f830cb…a1cbdece3a9f73

1 in → 1 out8.3504 XPM116 B

ANSXnLY2…Sd25TjkD

1175ccba8973f7…a0065aa7cdcfda

1 in → 2 out8.2800 XPM226 B

AeEDfWAm…14mZJ7ea AMx9mTdJ…UwM1tSSA

47522a51bc7bcf…b414a945f47204

1 in → 2 out8.2800 XPM225 B

ANgBeK5V…MwFVPuNb ATNigJi1…EH6t1JCN

842bf9e48d6ebd…37879252b92d86

1 in → 2 out0.0381 XPM226 B

AZLXUxnV…qy95m5cS AN9N5HZ7…naQjwiCt

d2628324e870d2…81f2cd1e80bf49

1 in → 1 out0.0105 XPM191 B

Ad5XK22r…EYKsEjex

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.

1.068 × 10⁹⁶(97-digit number)

10681810753579894669…49126132375315335679

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

1.068 × 10⁹⁶(97-digit number)

10681810753579894669…49126132375315335679

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.068 × 10⁹⁶(97-digit number)

10681810753579894669…49126132375315335681

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

2.136 × 10⁹⁶(97-digit number)

21363621507159789339…98252264750630671359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.136 × 10⁹⁶(97-digit number)

21363621507159789339…98252264750630671361

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

4.272 × 10⁹⁶(97-digit number)

42727243014319578679…96504529501261342719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.272 × 10⁹⁶(97-digit number)

42727243014319578679…96504529501261342721

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

8.545 × 10⁹⁶(97-digit number)

85454486028639157359…93009059002522685439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.545 × 10⁹⁶(97-digit number)

85454486028639157359…93009059002522685441

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

1.709 × 10⁹⁷(98-digit number)

17090897205727831471…86018118005045370879

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.709 × 10⁹⁷(98-digit number)

17090897205727831471…86018118005045370881

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 #853,766

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