Block #610,532

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 7/1/2014, 6:15:07 PM · Difficulty 10.9175 · 6,199,872 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

35ce7a827ce2112c2e8a2f7f14f5413021e41a66ae932e8ae7681cbd80b54faf

View on Chainz ↗

Height

#610,532

Difficulty

10.917502

Transactions

Size

1.15 KB

Version

Bits

0aeae16e

Nonce

359,487,444

Timestamp

7/1/2014, 6:15:07 PM

Confirmations

6,199,872

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

7617c0a9f324a59ffa48799f60667d2591b1a1a3f6e6b87db26338bb4d572650

Transactions (4)

Coinbase4a6f672ef2cc8c…26456b1769ede0

1 in → 1 out8.4100 XPM116 B

ANSXnLY2…Sd25TjkD

a5ec61aeb1ad79…9b98d3fc6975d0

1 in → 2 out8.3700 XPM226 B

AYz8XXeX…wUExhw54 AUFeXgDG…9ZYq52sQ

6327bec4331590…21d5eff403ea84

1 in → 2 out7.3569 XPM226 B

Ae2e83MX…bzxmuQ39 AVqxuruh…kRULUwvY

0f4dc7e784211f…2881fc3a6b6376

3 in → 2 out5.9622 XPM522 B

AHkz5MhU…zjnMC7p7 Aa9TdDYz…3oKRZ7Es

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.

1.417 × 10⁹⁹(100-digit number)

14177289262523104544…86491512417328701439

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

1.417 × 10⁹⁹(100-digit number)

14177289262523104544…86491512417328701439

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.417 × 10⁹⁹(100-digit number)

14177289262523104544…86491512417328701441

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

2.835 × 10⁹⁹(100-digit number)

28354578525046209089…72983024834657402879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.835 × 10⁹⁹(100-digit number)

28354578525046209089…72983024834657402881

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

5.670 × 10⁹⁹(100-digit number)

56709157050092418179…45966049669314805759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.670 × 10⁹⁹(100-digit number)

56709157050092418179…45966049669314805761

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

1.134 × 10¹⁰⁰(101-digit number)

11341831410018483635…91932099338629611519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.134 × 10¹⁰⁰(101-digit number)

11341831410018483635…91932099338629611521

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

2.268 × 10¹⁰⁰(101-digit number)

22683662820036967271…83864198677259223039

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.268 × 10¹⁰⁰(101-digit number)

22683662820036967271…83864198677259223041

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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

Block #610,532

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