Block #1,594,463

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/21/2016, 9:04:40 PM · Difficulty 10.6260 · 5,232,435 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ea1510c87ed242eac69365578bbeb219fb0b02088a8eb925a6a3c906e95bfb79

View on Chainz ↗

Height

#1,594,463

Difficulty

10.625989

Transactions

Size

1.18 KB

Version

Bits

0aa040cd

Nonce

1,838,781,362

Timestamp

5/21/2016, 9:04:40 PM

Confirmations

5,232,435

Mined by

⛏️ P2SHAV3PUmtuWNwuuXknmjMrMRS1cfAwNY8J6d

Merkle Root

d89abba8a798f5f0c35774144724947e5d6ee1716c84ad29bc6cfcebec1c0323

Transactions (2)

Coinbasee6a7c252d46128…b251c8d10df940

1 in → 1 out8.8600 XPM109 B

AV3PUmtu…AwNY8J6d

2ed43a2304affb…e9221a24ac0d35

1 in → 25 out69.8088 XPM1007 B

AY2qu7Yt…Tz81eP1J ARM6k7wL…sZ48m8mA AGTmjC3H…fMeuSRuQ AW1UezKJ…yyWeSMc5 ARbmELZZ…D2EmA9eK

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.

4.791 × 10⁹⁵(96-digit number)

47911256625275245124…53976147669680127999

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

4.791 × 10⁹⁵(96-digit number)

47911256625275245124…53976147669680127999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.791 × 10⁹⁵(96-digit number)

47911256625275245124…53976147669680128001

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

9.582 × 10⁹⁵(96-digit number)

95822513250550490248…07952295339360255999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.582 × 10⁹⁵(96-digit number)

95822513250550490248…07952295339360256001

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

1.916 × 10⁹⁶(97-digit number)

19164502650110098049…15904590678720511999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.916 × 10⁹⁶(97-digit number)

19164502650110098049…15904590678720512001

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

3.832 × 10⁹⁶(97-digit number)

38329005300220196099…31809181357441023999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.832 × 10⁹⁶(97-digit number)

38329005300220196099…31809181357441024001

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

7.665 × 10⁹⁶(97-digit number)

76658010600440392198…63618362714882047999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.665 × 10⁹⁶(97-digit number)

76658010600440392198…63618362714882048001

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 #1,594,463

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