Block #2,270,333

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 8/27/2017, 1:17:23 PM · Difficulty 10.9528 · 4,568,461 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3f783f52bc3db75b0faacd9254a67efa4f386377bc9d75994f6447079dbe33f2

View on Chainz ↗

Height

#2,270,333

Difficulty

10.952776

Transactions

Size

723 B

Version

Bits

0af3e91a

Nonce

66,234,127

Timestamp

8/27/2017, 1:17:23 PM

Confirmations

4,568,461

Mined by

⛏️ P2SHAN9DR8SLxJPcbRzuN1KAWs9jreZwEBDpRP

Merkle Root

c3865cf7359cb9c2fdd2ab901b73f3a20461dd2b4ab4165bfba6c3853b665dd1

Transactions (2)

Coinbase6402b5660409e4…40072105533c6e

1 in → 1 out8.3300 XPM110 B

AN9DR8SL…ZwEBDpRP

cb6ceadcf38668…a3ca75ce338115

3 in → 2 out2294.7500 XPM522 B

AXKyJvZX…Hzifn7of AViBaKwf…3Xk3qwK8

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.

1.470 × 10⁹⁷(98-digit number)

14704861069823956850…87558574263223334399

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

1.470 × 10⁹⁷(98-digit number)

14704861069823956850…87558574263223334399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.470 × 10⁹⁷(98-digit number)

14704861069823956850…87558574263223334401

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

2.940 × 10⁹⁷(98-digit number)

29409722139647913700…75117148526446668799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.940 × 10⁹⁷(98-digit number)

29409722139647913700…75117148526446668801

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

5.881 × 10⁹⁷(98-digit number)

58819444279295827400…50234297052893337599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.881 × 10⁹⁷(98-digit number)

58819444279295827400…50234297052893337601

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

1.176 × 10⁹⁸(99-digit number)

11763888855859165480…00468594105786675199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.176 × 10⁹⁸(99-digit number)

11763888855859165480…00468594105786675201

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

2.352 × 10⁹⁸(99-digit number)

23527777711718330960…00937188211573350399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.352 × 10⁹⁸(99-digit number)

23527777711718330960…00937188211573350401

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 #2,270,333

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