Block #1,587,851

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/17/2016, 1:08:45 AM · Difficulty 10.6504 · 5,239,126 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

bca3193c72a6cdf5cab0af3ef84a084250bd56d913e23879efc4e570406a9daf

View on Chainz ↗

Height

#1,587,851

Difficulty

10.650375

Transactions

Size

970 B

Version

Bits

0aa67f01

Nonce

1,863,397,748

Timestamp

5/17/2016, 1:08:45 AM

Confirmations

5,239,126

Mined by

⛏️ P2SHAXfXA9CaZnfYgCiyvxzP8jqySvzZNggkDB

Merkle Root

e741541d550564f53e43e55317da62e26b40e378704f13213307e3f62d88a82c

Transactions (2)

Coinbase935a5ce82fb8c9…06d4a528c92f68

1 in → 1 out8.8100 XPM110 B

AXfXA9Ca…zZNggkDB

ced1f2dcfe9f38…974de8a50ca7a1

1 in → 18 out27.2805 XPM770 B

ASwncKHm…gjcC3Skf AbwijVU5…qRbvEC24 AYbpqyGy…d2R9an1g AJdFVNXw…pyeMC1s9 AXBKutmg…VkhQ3V6t

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.

6.593 × 10⁹⁵(96-digit number)

65931596328951435000…85523764134576827199

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

6.593 × 10⁹⁵(96-digit number)

65931596328951435000…85523764134576827199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.593 × 10⁹⁵(96-digit number)

65931596328951435000…85523764134576827201

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

1.318 × 10⁹⁶(97-digit number)

13186319265790287000…71047528269153654399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.318 × 10⁹⁶(97-digit number)

13186319265790287000…71047528269153654401

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

2.637 × 10⁹⁶(97-digit number)

26372638531580574000…42095056538307308799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.637 × 10⁹⁶(97-digit number)

26372638531580574000…42095056538307308801

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

5.274 × 10⁹⁶(97-digit number)

52745277063161148000…84190113076614617599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.274 × 10⁹⁶(97-digit number)

52745277063161148000…84190113076614617601

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

1.054 × 10⁹⁷(98-digit number)

10549055412632229600…68380226153229235199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.054 × 10⁹⁷(98-digit number)

10549055412632229600…68380226153229235201

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 #1,587,851

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