Block #64,596

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/19/2013, 8:13:00 AM · Difficulty 8.9821 · 6,739,317 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

41b7b897864ebe4699a9086cceba09e21752756e80eac7df9d06645dd7c6a339

View on Chainz ↗

Height

#64,596

Difficulty

8.982097

Transactions

Size

726 B

Version

Bits

08fb6ab9

Nonce

258

Timestamp

7/19/2013, 8:13:00 AM

Confirmations

6,739,317

Mined by

⛏️ P2SHAUtmFi4sen9ycV18rscPTziMwLq1RTiLV3

Merkle Root

239733cb52973d757cf41c904fc411fd47538b68d7962ae59e32ed1b0737f538

Transactions (2)

Coinbasef831448a8cd28b…a0c5d6421c44ed

1 in → 1 out12.3900 XPM110 B

AUtmFi4s…q1RTiLV3

7f43d8bdfbb951…bd70c34fd91c22

3 in → 2 out114.0300 XPM520 B

AGpBLbTY…XyhUFmrh ATfgHoT7…uwChsUmK

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.

5.989 × 10¹⁰⁸(109-digit number)

59891819564691684607…17528382239995440019

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

5.989 × 10¹⁰⁸(109-digit number)

59891819564691684607…17528382239995440019

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.989 × 10¹⁰⁸(109-digit number)

59891819564691684607…17528382239995440021

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

1.197 × 10¹⁰⁹(110-digit number)

11978363912938336921…35056764479990880039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.197 × 10¹⁰⁹(110-digit number)

11978363912938336921…35056764479990880041

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

2.395 × 10¹⁰⁹(110-digit number)

23956727825876673843…70113528959981760079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.395 × 10¹⁰⁹(110-digit number)

23956727825876673843…70113528959981760081

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

4.791 × 10¹⁰⁹(110-digit number)

47913455651753347686…40227057919963520159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.791 × 10¹⁰⁹(110-digit number)

47913455651753347686…40227057919963520161

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

9.582 × 10¹⁰⁹(110-digit number)

95826911303506695372…80454115839927040319

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