Block #637,619

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 7/17/2014, 9:25:22 PM · Difficulty 10.9624 · 6,178,527 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f9cc971d2f22f0c0df7b4c4ed204ebd87074231027a1bc3a8523020f4916e968

View on Chainz ↗

Height

#637,619

Difficulty

10.962355

Transactions

Size

957 B

Version

Bits

0af65ce7

Nonce

1,558,404,588

Timestamp

7/17/2014, 9:25:22 PM

Confirmations

6,178,527

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

3f80a36cbeda966ad6a2b0c77381d94caccc6d222c9c7091440a41f553e36d3c

Transactions (3)

Coinbaseed7428b9fd17e4…9d3f18467cbb74

1 in → 1 out8.3300 XPM116 B

ANSXnLY2…Sd25TjkD

750c4e7762701a…7851e82b773a48

3 in → 2 out10.0817 XPM523 B

AZvJCXJr…L1ywp1Ht ANNBoEaA…o6TzGWqw

65884ec564a8e2…2ede78ee54783a

1 in → 2 out2.2288 XPM226 B

AMQouc2L…hPcwsqSs AWEm1NVx…BSyUpTdF

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.

1.643 × 10⁹⁹(100-digit number)

16438258102285563475…58471349572294082559

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

1.643 × 10⁹⁹(100-digit number)

16438258102285563475…58471349572294082559

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.643 × 10⁹⁹(100-digit number)

16438258102285563475…58471349572294082561

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

3.287 × 10⁹⁹(100-digit number)

32876516204571126951…16942699144588165119

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.287 × 10⁹⁹(100-digit number)

32876516204571126951…16942699144588165121

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

6.575 × 10⁹⁹(100-digit number)

65753032409142253903…33885398289176330239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.575 × 10⁹⁹(100-digit number)

65753032409142253903…33885398289176330241

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

1.315 × 10¹⁰⁰(101-digit number)

13150606481828450780…67770796578352660479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.315 × 10¹⁰⁰(101-digit number)

13150606481828450780…67770796578352660481

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

2.630 × 10¹⁰⁰(101-digit number)

26301212963656901561…35541593156705320959

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.630 × 10¹⁰⁰(101-digit number)

26301212963656901561…35541593156705320961

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

5.260 × 10¹⁰⁰(101-digit number)

52602425927313803123…71083186313410641919

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 #637,619

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