Block #83,168

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/25/2013, 11:16:19 PM · Difficulty 9.2693 · 6,708,008 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e1cadab97adae49253abb74e7865ed9004f384d383f27ff0d728dca66559eb7e

View on Chainz ↗

Height

#83,168

Difficulty

9.269285

Transactions

Size

626 B

Version

Bits

0944efde

Nonce

478

Timestamp

7/25/2013, 11:16:19 PM

Confirmations

6,708,008

Merkle Root

4a1e6b492bb50bda1bc3b98e508b29c24eed50f51f1ec119bc9751420483618a

Transactions (2)

Coinbase6f8c86f0daa6c7…229a9fd41f4e77

1 in → 1 out11.6300 XPM110 B

AbqCsm95…hKzwTSMe

3ddc72e70f67b8…47c2742541e693

3 in → 1 out23.5800 XPM419 B

AMmUy3x3…qPezWtyV

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.

2.828 × 10¹¹²(113-digit number)

28285769594620001264…36311715263782912849

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

2.828 × 10¹¹²(113-digit number)

28285769594620001264…36311715263782912849

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.828 × 10¹¹²(113-digit number)

28285769594620001264…36311715263782912851

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

5.657 × 10¹¹²(113-digit number)

56571539189240002529…72623430527565825699

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.657 × 10¹¹²(113-digit number)

56571539189240002529…72623430527565825701

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

1.131 × 10¹¹³(114-digit number)

11314307837848000505…45246861055131651399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.131 × 10¹¹³(114-digit number)

11314307837848000505…45246861055131651401

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

2.262 × 10¹¹³(114-digit number)

22628615675696001011…90493722110263302799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.262 × 10¹¹³(114-digit number)

22628615675696001011…90493722110263302801

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

4.525 × 10¹¹³(114-digit number)

45257231351392002023…80987444220526605599

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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