Block #84,608

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/26/2013, 10:46:42 PM · Difficulty 9.2733 · 6,714,844 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

351f668f279d4c8c40aad21a6f4f33846c78f1da50d27400e2b15f0bfaa3b562

View on Chainz ↗

Height

#84,608

Difficulty

9.273272

Transactions

Size

429 B

Version

Bits

0945f527

Nonce

2,995

Timestamp

7/26/2013, 10:46:42 PM

Confirmations

6,714,844

Mined by

⛏️ P2SHAY4DcQah2456yf3SzyMcyYYxjaaeMTqrZZ

Merkle Root

5b1d889507097a0974432201ad9f37ead8ee799ea0d41697b06b09ef6837bced

Transactions (2)

Coinbasec025d780a1bfc0…295eff161b4d18

1 in → 1 out11.6200 XPM109 B

AY4DcQah…aeMTqrZZ

eb1973b3c18309…50ddae7398a0b2

1 in → 2 out1.7100 XPM227 B

ARx4bG4A…CdNNNXiy AZs8hJYh…vxZmKFZt

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.

1.223 × 10¹⁰²(103-digit number)

12234164863732369932…16631014813477350089

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

1.223 × 10¹⁰²(103-digit number)

12234164863732369932…16631014813477350089

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.223 × 10¹⁰²(103-digit number)

12234164863732369932…16631014813477350091

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

2.446 × 10¹⁰²(103-digit number)

24468329727464739864…33262029626954700179

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.446 × 10¹⁰²(103-digit number)

24468329727464739864…33262029626954700181

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

4.893 × 10¹⁰²(103-digit number)

48936659454929479728…66524059253909400359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.893 × 10¹⁰²(103-digit number)

48936659454929479728…66524059253909400361

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

9.787 × 10¹⁰²(103-digit number)

97873318909858959457…33048118507818800719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.787 × 10¹⁰²(103-digit number)

97873318909858959457…33048118507818800721

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

1.957 × 10¹⁰³(104-digit number)

19574663781971791891…66096237015637601439

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