Block #3,300,220

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 8/7/2019, 2:38:13 PM · Difficulty 10.9957 · 3,507,778 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

16c107b9891a04b8ac02f91d1deef0f4e4340ecdd17c9140633ec18ddddf2405

View on Chainz ↗

Height

#3,300,220

Difficulty

10.995702

Transactions

Size

652 B

Version

Bits

0afee659

Nonce

1,155,803,757

Timestamp

8/7/2019, 2:38:13 PM

Confirmations

3,507,778

Mined by

⛏️ P2SHASiq2qtKTzQ7sbERFE8Jp8HjsgVMhmk7yL

Merkle Root

c79c3a5e11dc7753faa86b35eff166dc341d04ef18200e4d2545dc507dd7097e

Transactions (3)

Coinbase6dbbb558968b02…808d4d98a2e5b1

1 in → 1 out8.2800 XPM110 B

ASiq2qtK…VMhmk7yL

a5dd2f483898de…400f0da337d9f4

1 in → 2 out299.6200 XPM225 B

AXfJqzUb…HXeXmjMz APDUaFAD…5DAc3Ti1

860e534f1aa052…85011c09f42aa8

1 in → 2 out295.6100 XPM226 B

AXfJqzUb…HXeXmjMz APpTpGhZ…fLioJSac

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.

1.169 × 10⁹⁸(99-digit number)

11693523449009083077…29180368483830087679

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

1.169 × 10⁹⁸(99-digit number)

11693523449009083077…29180368483830087679

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.169 × 10⁹⁸(99-digit number)

11693523449009083077…29180368483830087681

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

2.338 × 10⁹⁸(99-digit number)

23387046898018166154…58360736967660175359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.338 × 10⁹⁸(99-digit number)

23387046898018166154…58360736967660175361

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

4.677 × 10⁹⁸(99-digit number)

46774093796036332308…16721473935320350719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.677 × 10⁹⁸(99-digit number)

46774093796036332308…16721473935320350721

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

9.354 × 10⁹⁸(99-digit number)

93548187592072664616…33442947870640701439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.354 × 10⁹⁸(99-digit number)

93548187592072664616…33442947870640701441

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

1.870 × 10⁹⁹(100-digit number)

18709637518414532923…66885895741281402879

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.870 × 10⁹⁹(100-digit number)

18709637518414532923…66885895741281402881

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 #3,300,220

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