Block #627,911

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 7/11/2014, 6:38:13 AM · Difficulty 10.9606 · 6,178,533 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f278a0f8a686ff8a46da551cc8391dc4814f1b9973e45db5bcd7111be3719f4c

View on Chainz ↗

Height

#627,911

Difficulty

10.960636

Transactions

Size

767 B

Version

Bits

0af5ec44

Nonce

6,066

Timestamp

7/11/2014, 6:38:13 AM

Confirmations

6,178,533

Mined by

⛏️ aSAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

d87cc909a0ac8582aafc33bf0e191301948d23e027b554888a204cc683f06236

Transactions (1)

Coinbased87cc909a0ac85…204cc683f06236

1 in → 18 out8.3084 XPM675 B

AQvZBsUo…hppgRZTJ AJzWx2VD…j4ZSMit5 AQyr8Lw3…hs4nt3Pn Ae7UyoY4…DtgAv9cY AJCeFGQe…Ab2py48B

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.

5.329 × 10⁹⁹(100-digit number)

53294824863234099252…53132832659351478079

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

5.329 × 10⁹⁹(100-digit number)

53294824863234099252…53132832659351478079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.329 × 10⁹⁹(100-digit number)

53294824863234099252…53132832659351478081

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

1.065 × 10¹⁰⁰(101-digit number)

10658964972646819850…06265665318702956159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.065 × 10¹⁰⁰(101-digit number)

10658964972646819850…06265665318702956161

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

2.131 × 10¹⁰⁰(101-digit number)

21317929945293639700…12531330637405912319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.131 × 10¹⁰⁰(101-digit number)

21317929945293639700…12531330637405912321

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

4.263 × 10¹⁰⁰(101-digit number)

42635859890587279401…25062661274811824639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.263 × 10¹⁰⁰(101-digit number)

42635859890587279401…25062661274811824641

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

8.527 × 10¹⁰⁰(101-digit number)

85271719781174558803…50125322549623649279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.527 × 10¹⁰⁰(101-digit number)

85271719781174558803…50125322549623649281

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

1.705 × 10¹⁰¹(102-digit number)

17054343956234911760…00250645099247298559

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 #627,911

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