Block #62,277

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/18/2013, 6:10:12 PM · Difficulty 8.9759 · 6,730,186 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2b4f782bf1e14d48d4cd485c637cf1e252acc200d5fbc1e9081ed817f2999c21

View on Chainz ↗

Height

#62,277

Difficulty

8.975919

Transactions

Size

947 B

Version

Bits

08f9d5d7

Nonce

174

Timestamp

7/18/2013, 6:10:12 PM

Confirmations

6,730,186

Merkle Root

fd9e5f8076292b5a6484f43d440770e1ff917a21658f3a1c51530aa87ebb20b7

Transactions (3)

Coinbase558bd4b63a21ab…51560452eeca25

1 in → 1 out12.4100 XPM110 B

AZhqXzMq…sMSP4iwP

cc5835cb2f3e78…d89ea235c48fc8

2 in → 2 out173.3337 XPM375 B

AYcRcaf6…BXEABkji AcqWv4eQ…d5eyCXr3

6a67d1561a1adf…56f25891c0bcf9

2 in → 2 out2.1900 XPM374 B

AcDmKYR3…brUcutjF AHb9ZoMv…uYnTVCE4

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.

1.744 × 10⁹⁰(91-digit number)

17440310301688168073…88276382451871854299

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

1.744 × 10⁹⁰(91-digit number)

17440310301688168073…88276382451871854299

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.744 × 10⁹⁰(91-digit number)

17440310301688168073…88276382451871854301

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

3.488 × 10⁹⁰(91-digit number)

34880620603376336146…76552764903743708599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.488 × 10⁹⁰(91-digit number)

34880620603376336146…76552764903743708601

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

6.976 × 10⁹⁰(91-digit number)

69761241206752672293…53105529807487417199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.976 × 10⁹⁰(91-digit number)

69761241206752672293…53105529807487417201

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

1.395 × 10⁹¹(92-digit number)

13952248241350534458…06211059614974834399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.395 × 10⁹¹(92-digit number)

13952248241350534458…06211059614974834401

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

2.790 × 10⁹¹(92-digit number)

27904496482701068917…12422119229949668799

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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 9

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