Block #61,923

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/18/2013, 4:05:38 PM · Difficulty 8.9748 · 6,727,916 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

041e75f4c0e4a8f2e6223b4b2945b2e8ea6dfb909b74d21e97800b4211278404

View on Chainz ↗

Height

#61,923

Difficulty

8.974785

Transactions

Size

1.51 KB

Version

Bits

08f98b88

Nonce

670

Timestamp

7/18/2013, 4:05:38 PM

Confirmations

6,727,916

Merkle Root

e5dac302ef654de4377a1dd7a1ff6eac0e3a99013a8474d98e81dafb731c37aa

Transactions (3)

Coinbase0e23d447797337…37470ee9a8b60e

1 in → 1 out12.4200 XPM110 B

ARwVAxRj…s2qJ8LMQ

01bbb48ea79d62…253531a57fb376

5 in → 2 out328.7362 XPM820 B

AKgT5mR1…oNdw1Ckv AeG2cBFR…RBcK65jf

eeebcdac40b7b8…eb4198f5a4e256

3 in → 2 out99.8187 XPM522 B

AaciXbyr…vkSeVXFV AKeqHKgf…5e2nvGoy

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.

4.824 × 10⁹⁷(98-digit number)

48249173930974603184…84052307357697373579

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

4.824 × 10⁹⁷(98-digit number)

48249173930974603184…84052307357697373579

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.824 × 10⁹⁷(98-digit number)

48249173930974603184…84052307357697373581

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

9.649 × 10⁹⁷(98-digit number)

96498347861949206368…68104614715394747159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.649 × 10⁹⁷(98-digit number)

96498347861949206368…68104614715394747161

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

1.929 × 10⁹⁸(99-digit number)

19299669572389841273…36209229430789494319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.929 × 10⁹⁸(99-digit number)

19299669572389841273…36209229430789494321

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

3.859 × 10⁹⁸(99-digit number)

38599339144779682547…72418458861578988639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.859 × 10⁹⁸(99-digit number)

38599339144779682547…72418458861578988641

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

7.719 × 10⁹⁸(99-digit number)

77198678289559365094…44836917723157977279

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