Block #105,435

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/8/2013, 12:47:27 PM · Difficulty 9.5839 · 6,705,066 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

71efca664d21ade83abc8645b0318053c37af8ce32e1a0ad78ce995bb8f8dd84

View on Chainz ↗

Height

#105,435

Difficulty

9.583885

Transactions

Size

358 B

Version

Bits

09957985

Nonce

499,413

Timestamp

8/8/2013, 12:47:27 PM

Confirmations

6,705,066

Mined by

⛏️ P2SHANCytZECNWymRVghMjCPA33jUjWrgRVYNM

Merkle Root

f27c2f6e28c622bc7f3c32ece023251da383d45dc030a11e0a4f5092ee26b149

Transactions (2)

Coinbase45d974ad4e7dc5…df38ae34c56e7a

1 in → 1 out10.8800 XPM109 B

ANCytZEC…WrgRVYNM

ec1fe9d34a56ec…2950b7b4816600

1 in → 1 out11.1500 XPM158 B

ATareS7a…5FKKTQVH

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.

1.760 × 10⁹⁸(99-digit number)

17609061083162033555…89597592381472336149

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

1.760 × 10⁹⁸(99-digit number)

17609061083162033555…89597592381472336149

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.760 × 10⁹⁸(99-digit number)

17609061083162033555…89597592381472336151

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

3.521 × 10⁹⁸(99-digit number)

35218122166324067110…79195184762944672299

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.521 × 10⁹⁸(99-digit number)

35218122166324067110…79195184762944672301

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

7.043 × 10⁹⁸(99-digit number)

70436244332648134220…58390369525889344599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.043 × 10⁹⁸(99-digit number)

70436244332648134220…58390369525889344601

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

1.408 × 10⁹⁹(100-digit number)

14087248866529626844…16780739051778689199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.408 × 10⁹⁹(100-digit number)

14087248866529626844…16780739051778689201

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

2.817 × 10⁹⁹(100-digit number)

28174497733059253688…33561478103557378399

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

Block #105,435

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