Block #613,863

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 7/3/2014, 7:17:14 AM · Difficulty 10.9339 · 6,181,988 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

55bff69491d69ba78a3540227526db5deb8b3efb336be850ea9eab3ef9260533

View on Chainz ↗

Height

#613,863

Difficulty

10.933919

Transactions

Size

1.23 KB

Version

Bits

0aef1555

Nonce

318,312,504

Timestamp

7/3/2014, 7:17:14 AM

Confirmations

6,181,988

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

8c14f044e3751b88d9b35fc3cfa9f54fca7a3c4abee861f4bf378bfe38b84385

Transactions (5)

Coinbase6992af39486540…623fc55e428fb2

1 in → 1 out8.3900 XPM116 B

ANSXnLY2…Sd25TjkD

84fb217a7c98bc…90798339ba8a80

2 in → 2 out12.4033 XPM375 B

AWFAErX5…rsHG6Xi9 AHdkjDnS…SYJhF91Y

04fb5692490025…96956444e59e2b

1 in → 2 out8.3700 XPM226 B

AHgMG19r…jjNsLbgW ASrYeiHQ…GZsXQfSy

1ab097578b9748…36f967ceb5f5f7

1 in → 2 out8.3700 XPM226 B

AbxgKwWg…DCgcssS6 AZEtDkob…12eJC5nb

6bdf0b3b013c54…607fefbc9d5655

1 in → 2 out7.3514 XPM227 B

AL6XDbit…Uix7CJBt Aa6m331p…NVBR9cYG

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.

1.105 × 10⁹⁹(100-digit number)

11053089683668410851…57358851328066846719

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

1.105 × 10⁹⁹(100-digit number)

11053089683668410851…57358851328066846719

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.105 × 10⁹⁹(100-digit number)

11053089683668410851…57358851328066846721

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

2.210 × 10⁹⁹(100-digit number)

22106179367336821702…14717702656133693439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.210 × 10⁹⁹(100-digit number)

22106179367336821702…14717702656133693441

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

4.421 × 10⁹⁹(100-digit number)

44212358734673643404…29435405312267386879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.421 × 10⁹⁹(100-digit number)

44212358734673643404…29435405312267386881

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

8.842 × 10⁹⁹(100-digit number)

88424717469347286809…58870810624534773759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.842 × 10⁹⁹(100-digit number)

88424717469347286809…58870810624534773761

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

1.768 × 10¹⁰⁰(101-digit number)

17684943493869457361…17741621249069547519

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.768 × 10¹⁰⁰(101-digit number)

17684943493869457361…17741621249069547521

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

3.536 × 10¹⁰⁰(101-digit number)

35369886987738914723…35483242498139095039

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