Block #71,577

TWNLength 8★☆☆☆☆

Bi-Twin Chain · Discovered 7/20/2013, 7:25:22 PM · Difficulty 8.9933 · 6,719,841 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

96baaa31e8de8e07c2326d3f5ef9edda10a274e888ee7ba57a51ed001b1ce6bb

View on Chainz ↗

Height

#71,577

Difficulty

8.993321

Transactions

Size

205 B

Version

Bits

08fe4a4a

Nonce

574

Timestamp

7/20/2013, 7:25:22 PM

Confirmations

6,719,841

Merkle Root

c719cc9e72464eff02fffb35da7ea513e38bdad48c168db42672bf99b83678db

Transactions (1)

Coinbasec719cc9e72464e…72bf99b83678db

1 in → 1 out12.3500 XPM110 B

ANCYL9xh…9WyGnqDE

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.

1.083 × 10¹⁰⁷(108-digit number)

10837583176137084214…81253042044594320039

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

1.083 × 10¹⁰⁷(108-digit number)

10837583176137084214…81253042044594320039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.083 × 10¹⁰⁷(108-digit number)

10837583176137084214…81253042044594320041

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

2.167 × 10¹⁰⁷(108-digit number)

21675166352274168429…62506084089188640079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.167 × 10¹⁰⁷(108-digit number)

21675166352274168429…62506084089188640081

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

4.335 × 10¹⁰⁷(108-digit number)

43350332704548336858…25012168178377280159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.335 × 10¹⁰⁷(108-digit number)

43350332704548336858…25012168178377280161

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

8.670 × 10¹⁰⁷(108-digit number)

86700665409096673717…50024336356754560319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.670 × 10¹⁰⁷(108-digit number)

86700665409096673717…50024336356754560321

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 8 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

CommonChain length 8

Found in most blocks. The baseline for Primecoin's proof-of-work.

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