Block #65,847

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/19/2013, 2:19:04 PM · Difficulty 8.9850 · 6,725,618 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8c8117e45f0acd52d51b9c103d4e8fcc93e30614cdcc0c4169a52e6ae0e70ca7

View on Chainz ↗

Height

#65,847

Difficulty

8.985014

Transactions

Size

982 B

Version

Bits

08fc29e0

Nonce

134

Timestamp

7/19/2013, 2:19:04 PM

Confirmations

6,725,618

Merkle Root

3ddbafaa01600dfc69d877daac3befbf53c09505bccdcc1eb90974674942898c

Transactions (2)

Coinbaseefb1163b3c9fb4…e937552225f3de

1 in → 1 out12.3800 XPM110 B

AZQ2N8LZ…fcMJoTdP

47ae65672b2f99…ffaf39f59b18f3

5 in → 1 out500.0000 XPM783 B

AP4isPk7…tyyEi75Z

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.

3.470 × 10⁹¹(92-digit number)

34701392857469416911…08836004244144808399

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

3.470 × 10⁹¹(92-digit number)

34701392857469416911…08836004244144808399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.470 × 10⁹¹(92-digit number)

34701392857469416911…08836004244144808401

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

6.940 × 10⁹¹(92-digit number)

69402785714938833822…17672008488289616799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.940 × 10⁹¹(92-digit number)

69402785714938833822…17672008488289616801

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

1.388 × 10⁹²(93-digit number)

13880557142987766764…35344016976579233599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.388 × 10⁹²(93-digit number)

13880557142987766764…35344016976579233601

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

2.776 × 10⁹²(93-digit number)

27761114285975533528…70688033953158467199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.776 × 10⁹²(93-digit number)

27761114285975533528…70688033953158467201

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

5.552 × 10⁹²(93-digit number)

55522228571951067057…41376067906316934399

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