Block #2,318,204

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 10/2/2017, 12:36:38 AM · Difficulty 10.9131 · 4,525,832 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

9572ada4308eb0905320ace80afc05e444c78f1acb705a3f45e8cd3a07bfca3e

View on Chainz ↗

Height

#2,318,204

Difficulty

10.913072

Transactions

Size

904 B

Version

Bits

0ae9bf10

Nonce

111,484,269

Timestamp

10/2/2017, 12:36:38 AM

Confirmations

4,525,832

Mined by

⛏️ P2SHARKD65mEz998Z83i6XxGuZ5atGTSBf63k2

Merkle Root

0a1a664f24d7ef123c04f04ae112cd492a43d088da90a2545125c75de388b0ca

Transactions (2)

Coinbase18705d2058d000…c3415e49812794

1 in → 1 out8.3900 XPM109 B

ARKD65mE…TSBf63k2

4b7abd490f0837…058a07ad1e36f4

4 in → 3 out5741.1116 XPM704 B

ARLxMe9N…Bxx8GE18 AexxQu4T…H3bbSgnQ Abn6PFwV…n8jZxCtH

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.

1.196 × 10⁹⁸(99-digit number)

11962387213550811406…16586867027151093759

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

1.196 × 10⁹⁸(99-digit number)

11962387213550811406…16586867027151093759

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.196 × 10⁹⁸(99-digit number)

11962387213550811406…16586867027151093761

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

2.392 × 10⁹⁸(99-digit number)

23924774427101622813…33173734054302187519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.392 × 10⁹⁸(99-digit number)

23924774427101622813…33173734054302187521

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

4.784 × 10⁹⁸(99-digit number)

47849548854203245626…66347468108604375039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.784 × 10⁹⁸(99-digit number)

47849548854203245626…66347468108604375041

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

9.569 × 10⁹⁸(99-digit number)

95699097708406491253…32694936217208750079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.569 × 10⁹⁸(99-digit number)

95699097708406491253…32694936217208750081

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

1.913 × 10⁹⁹(100-digit number)

19139819541681298250…65389872434417500159

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.913 × 10⁹⁹(100-digit number)

19139819541681298250…65389872434417500161

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 #2,318,204

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