Block #1,587,281

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/16/2016, 3:41:32 PM · Difficulty 10.6502 · 5,251,472 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

bdc37fd4e764ceced6c6c40880289dcee025f0ab1f69c61eb0533d7eb4fadd84

View on Chainz ↗

Height

#1,587,281

Difficulty

10.650194

Transactions

Size

1019 B

Version

Bits

0aa6731c

Nonce

908,881,773

Timestamp

5/16/2016, 3:41:32 PM

Confirmations

5,251,472

Mined by

⛏️ P2SHAH2fCaeDBoY1Tp4KEmfke4PVi4z5ggiJfk

Merkle Root

fe7f7c9632f8572da5cf7155589ba06f64aca8bc3eae3065f77f7afdd955a2b6

Transactions (2)

Coinbasecf861da3ca904d…46e5adcd3e2a45

1 in → 1 out8.8100 XPM110 B

AH2fCaeD…z5ggiJfk

7b77c75147f685…e85cfde7eb3215

5 in → 2 out302.0861 XPM819 B

AarCBJcx…KSZ6QNaq AVrJxG6A…HLaZpfbp

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.

6.932 × 10⁹⁵(96-digit number)

69324764837137338170…31888595219848391679

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

6.932 × 10⁹⁵(96-digit number)

69324764837137338170…31888595219848391679

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.932 × 10⁹⁵(96-digit number)

69324764837137338170…31888595219848391681

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

1.386 × 10⁹⁶(97-digit number)

13864952967427467634…63777190439696783359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.386 × 10⁹⁶(97-digit number)

13864952967427467634…63777190439696783361

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

2.772 × 10⁹⁶(97-digit number)

27729905934854935268…27554380879393566719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.772 × 10⁹⁶(97-digit number)

27729905934854935268…27554380879393566721

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

5.545 × 10⁹⁶(97-digit number)

55459811869709870536…55108761758787133439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.545 × 10⁹⁶(97-digit number)

55459811869709870536…55108761758787133441

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

1.109 × 10⁹⁷(98-digit number)

11091962373941974107…10217523517574266879

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.109 × 10⁹⁷(98-digit number)

11091962373941974107…10217523517574266881

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

2.218 × 10⁹⁷(98-digit number)

22183924747883948214…20435047035148533759

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 #1,587,281

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