Block #160,466

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 9/11/2013, 11:05:11 PM · Difficulty 9.8608 · 6,630,532 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

fde01c7e91ee5d1f66a1854850f6c09e92dcca1e418ef698619e13e562ef0132

View on Chainz ↗

Height

#160,466

Difficulty

9.860785

Transactions

Size

196 B

Version

Bits

09dc5c6e

Nonce

68,706

Timestamp

9/11/2013, 11:05:11 PM

Confirmations

6,630,532

Merkle Root

544153c4741abdc644999f34ca782dbe25f4365e6108df648d9914de10640a02

Transactions (1)

Coinbase544153c4741abd…9914de10640a02

1 in → 1 out10.2700 XPM109 B

AX99MLNm…vtidqEwE

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.

6.342 × 10⁸⁷(88-digit number)

63426536126080004349…41015226854898462439

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

6.342 × 10⁸⁷(88-digit number)

63426536126080004349…41015226854898462439

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.342 × 10⁸⁷(88-digit number)

63426536126080004349…41015226854898462441

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

1.268 × 10⁸⁸(89-digit number)

12685307225216000869…82030453709796924879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.268 × 10⁸⁸(89-digit number)

12685307225216000869…82030453709796924881

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

2.537 × 10⁸⁸(89-digit number)

25370614450432001739…64060907419593849759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.537 × 10⁸⁸(89-digit number)

25370614450432001739…64060907419593849761

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

5.074 × 10⁸⁸(89-digit number)

50741228900864003479…28121814839187699519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.074 × 10⁸⁸(89-digit number)

50741228900864003479…28121814839187699521

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

1.014 × 10⁸⁹(90-digit number)

10148245780172800695…56243629678375399039

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