Block #207,060

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 10/13/2013, 5:24:56 AM · Difficulty 9.9017 · 6,596,243 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8efa61ce6774edd68241f8141141d93c42d3f2f89c9a719c500f8ab86a484647

View on Chainz ↗

Height

#207,060

Difficulty

9.901704

Transactions

Size

928 B

Version

Bits

09e6d60e

Nonce

3,222

Timestamp

10/13/2013, 5:24:56 AM

Confirmations

6,596,243

Mined by

⛏️ P2SHAQTxynFDuSPLD1xBsYoiHBqkNQJVWN5dRq

Merkle Root

a170223ad1d4f1c981023d6450645e5ce2ac1d18df0912ea6f44313da6f5bf25

Transactions (2)

Coinbasea4cd5068d6f375…9343834bcaeb05

1 in → 1 out10.1900 XPM109 B

AQTxynFD…JVWN5dRq

cc233c450737ab…9118f9e53bf26d

6 in → 1 out61.2300 XPM731 B

AZDw8GgW…GexTkqVt

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.

1.862 × 10⁸⁹(90-digit number)

18627247057858146783…29236766664665163549

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

1.862 × 10⁸⁹(90-digit number)

18627247057858146783…29236766664665163549

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.862 × 10⁸⁹(90-digit number)

18627247057858146783…29236766664665163551

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

3.725 × 10⁸⁹(90-digit number)

37254494115716293567…58473533329330327099

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.725 × 10⁸⁹(90-digit number)

37254494115716293567…58473533329330327101

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

7.450 × 10⁸⁹(90-digit number)

74508988231432587134…16947066658660654199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.450 × 10⁸⁹(90-digit number)

74508988231432587134…16947066658660654201

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

1.490 × 10⁹⁰(91-digit number)

14901797646286517426…33894133317321308399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.490 × 10⁹⁰(91-digit number)

14901797646286517426…33894133317321308401

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

2.980 × 10⁹⁰(91-digit number)

29803595292573034853…67788266634642616799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.980 × 10⁹⁰(91-digit number)

29803595292573034853…67788266634642616801

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