Block #162,660

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 9/13/2013, 11:20:38 AM · Difficulty 9.8614 · 6,663,992 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

789da8a670081fbb344dd51cc6a65794417df0998617bbbd29cbed29cf5d87e6

View on Chainz ↗

Height

#162,660

Difficulty

9.861415

Transactions

Size

199 B

Version

Bits

09dc85b2

Nonce

411,980

Timestamp

9/13/2013, 11:20:38 AM

Confirmations

6,663,992

Mined by

⛏️ P2SHAMLAAyBPCXhgaRf5xWtK31SsvxAobUBkWY

Merkle Root

a06f568ba1fbbe686258e20e226368f578f432c240ac678ace2ef48e5ce87ad4

Transactions (1)

Coinbasea06f568ba1fbbe…2ef48e5ce87ad4

1 in → 1 out10.2700 XPM109 B

AMLAAyBP…AobUBkWY

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.

5.055 × 10⁹⁵(96-digit number)

50559079356511407895…53240438119693817599

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

5.055 × 10⁹⁵(96-digit number)

50559079356511407895…53240438119693817599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.055 × 10⁹⁵(96-digit number)

50559079356511407895…53240438119693817601

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

1.011 × 10⁹⁶(97-digit number)

10111815871302281579…06480876239387635199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.011 × 10⁹⁶(97-digit number)

10111815871302281579…06480876239387635201

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

2.022 × 10⁹⁶(97-digit number)

20223631742604563158…12961752478775270399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.022 × 10⁹⁶(97-digit number)

20223631742604563158…12961752478775270401

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

4.044 × 10⁹⁶(97-digit number)

40447263485209126316…25923504957550540799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.044 × 10⁹⁶(97-digit number)

40447263485209126316…25923504957550540801

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

8.089 × 10⁹⁶(97-digit number)

80894526970418252632…51847009915101081599

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 #162,660

Cookie Preferences