Block #2,178,161

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 6/25/2017, 11:15:04 PM · Difficulty 10.9252 · 4,660,847 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ad04b8a2669e3df79426fa4e961fb5cd10dc82589b6e35e43f66c3b79f33f102

View on Chainz ↗

Height

#2,178,161

Difficulty

10.925184

Transactions

Size

424 B

Version

Bits

0aecd8e2

Nonce

189,761,557

Timestamp

6/25/2017, 11:15:04 PM

Confirmations

4,660,847

Mined by

⛏️ P2SHAchyDmbbnuKkT53Z8JwWtAxcrktrRizguL

Merkle Root

f21a50669eb1743629e838487e79f42e741c12ba27a683b6a0a936683ea44911

Transactions (2)

Coinbased927a3ee390854…dd1ddd043329c2

1 in → 1 out8.3700 XPM109 B

AchyDmbb…trRizguL

73b18d1832c3af…9e23b678527e74

1 in → 2 out312.7738 XPM225 B

Abe5k4Vz…RpC98JSY AN8szP8k…CGjYtVjh

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.

4.606 × 10⁹⁴(95-digit number)

46065877215159216105…24683093572738298599

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

4.606 × 10⁹⁴(95-digit number)

46065877215159216105…24683093572738298599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.606 × 10⁹⁴(95-digit number)

46065877215159216105…24683093572738298601

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

9.213 × 10⁹⁴(95-digit number)

92131754430318432210…49366187145476597199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.213 × 10⁹⁴(95-digit number)

92131754430318432210…49366187145476597201

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

1.842 × 10⁹⁵(96-digit number)

18426350886063686442…98732374290953194399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.842 × 10⁹⁵(96-digit number)

18426350886063686442…98732374290953194401

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

3.685 × 10⁹⁵(96-digit number)

36852701772127372884…97464748581906388799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.685 × 10⁹⁵(96-digit number)

36852701772127372884…97464748581906388801

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

7.370 × 10⁹⁵(96-digit number)

73705403544254745768…94929497163812777599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.370 × 10⁹⁵(96-digit number)

73705403544254745768…94929497163812777601

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 #2,178,161

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