Block #1,464,468

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/19/2016, 5:04:02 PM · Difficulty 10.7786 · 5,376,586 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

906d87c44238b6adcc92c9028af3d553d97a3b20fa23023682985f1898959c04

View on Chainz ↗

Height

#1,464,468

Difficulty

10.778560

Transactions

Size

1.11 KB

Version

Bits

0ac74fbd

Nonce

725,067,782

Timestamp

2/19/2016, 5:04:02 PM

Confirmations

5,376,586

Mined by

⛏️ P2SHAZEEdmgRPriANxo593juUDR6zdGCJKaMRB

Merkle Root

8ff571b7a8b63f24db8a5bfad6de5814bdb4a1323dbdbe0be02478af7579a2a1

Transactions (2)

Coinbase89b713054cdca1…9861ae010525d0

1 in → 1 out8.6000 XPM109 B

AZEEdmgR…GCJKaMRB

be53f74f98d638…727f5f4db2d640

1 in → 23 out158.4789 XPM940 B

AMRvoQuL…5Dw7CEhj AXbqV9PY…Vo2Ekhd4 AM7CRoYu…aLmRiYRp ASwDgq5Y…Xmrka935 AN9431pP…qJwmE7ip

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.

1.172 × 10⁹⁷(98-digit number)

11725364890423950496…33255934679661088639

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

1.172 × 10⁹⁷(98-digit number)

11725364890423950496…33255934679661088639

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.172 × 10⁹⁷(98-digit number)

11725364890423950496…33255934679661088641

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

2.345 × 10⁹⁷(98-digit number)

23450729780847900992…66511869359322177279

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.345 × 10⁹⁷(98-digit number)

23450729780847900992…66511869359322177281

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

4.690 × 10⁹⁷(98-digit number)

46901459561695801984…33023738718644354559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.690 × 10⁹⁷(98-digit number)

46901459561695801984…33023738718644354561

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

9.380 × 10⁹⁷(98-digit number)

93802919123391603968…66047477437288709119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.380 × 10⁹⁷(98-digit number)

93802919123391603968…66047477437288709121

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

1.876 × 10⁹⁸(99-digit number)

18760583824678320793…32094954874577418239

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.876 × 10⁹⁸(99-digit number)

18760583824678320793…32094954874577418241

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 #1,464,468

Cookie Preferences