Block #93,161

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/2/2013, 5:47:37 AM · Difficulty 9.1969 · 6,697,826 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

0d2baa800a8853c3e1da355f22a0ba347b0ff1d21c59cbfe3ad1de03795a63a8

View on Chainz ↗

Height

#93,161

Difficulty

9.196928

Transactions

Size

203 B

Version

Bits

093269db

Nonce

18,779

Timestamp

8/2/2013, 5:47:37 AM

Confirmations

6,697,826

Merkle Root

aa0c7a6e53674f86785d951d093347d51d39caed8a678eb04a4dc9b76ac7f0de

Transactions (1)

Coinbaseaa0c7a6e53674f…4dc9b76ac7f0de

1 in → 1 out11.8100 XPM109 B

AcBadmkp…GmhL921o

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.

1.661 × 10¹⁰⁵(106-digit number)

16619634747859313366…23305442049867936479

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

1.661 × 10¹⁰⁵(106-digit number)

16619634747859313366…23305442049867936479

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.661 × 10¹⁰⁵(106-digit number)

16619634747859313366…23305442049867936481

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

3.323 × 10¹⁰⁵(106-digit number)

33239269495718626732…46610884099735872959

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.323 × 10¹⁰⁵(106-digit number)

33239269495718626732…46610884099735872961

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

6.647 × 10¹⁰⁵(106-digit number)

66478538991437253464…93221768199471745919

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.647 × 10¹⁰⁵(106-digit number)

66478538991437253464…93221768199471745921

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

1.329 × 10¹⁰⁶(107-digit number)

13295707798287450692…86443536398943491839

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.329 × 10¹⁰⁶(107-digit number)

13295707798287450692…86443536398943491841

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

2.659 × 10¹⁰⁶(107-digit number)

26591415596574901385…72887072797886983679

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