Block #2,634,307

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 4/28/2018, 8:19:31 PM · Difficulty 11.2376 · 4,197,419 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8b19fc8bb190e1b5c61361474ecd0ea15fadeddfd31cae74b5816d93b1c28c31

View on Chainz ↗

Height

#2,634,307

Difficulty

11.237620

Transactions

Size

723 B

Version

Bits

0b3cd4a8

Nonce

421,747,294

Timestamp

4/28/2018, 8:19:31 PM

Confirmations

4,197,419

Mined by

⛏️ P2SHASXrBNi1YJBZeFkARzzFGB5MZmKEQLF8u9

Merkle Root

b391d06e0417f1202edb6f7f9c76e2f94e8e9cc6f484802c2fe50529a7688589

Transactions (2)

Coinbasebe711d3152ba41…0494f53363aaf1

1 in → 1 out7.9200 XPM110 B

ASXrBNi1…KEQLF8u9

9a829d2c98c1ae…22cda0c8e7df96

3 in → 2 out162.0497 XPM521 B

AaNEwLUV…2FoEFBNV ARTGxeAc…WmRAvHDa

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.

3.796 × 10⁹⁹(100-digit number)

37968909163153704110…74133994450173624319

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

3.796 × 10⁹⁹(100-digit number)

37968909163153704110…74133994450173624319

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.796 × 10⁹⁹(100-digit number)

37968909163153704110…74133994450173624321

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

7.593 × 10⁹⁹(100-digit number)

75937818326307408221…48267988900347248639

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.593 × 10⁹⁹(100-digit number)

75937818326307408221…48267988900347248641

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

1.518 × 10¹⁰⁰(101-digit number)

15187563665261481644…96535977800694497279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.518 × 10¹⁰⁰(101-digit number)

15187563665261481644…96535977800694497281

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

3.037 × 10¹⁰⁰(101-digit number)

30375127330522963288…93071955601388994559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.037 × 10¹⁰⁰(101-digit number)

30375127330522963288…93071955601388994561

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

6.075 × 10¹⁰⁰(101-digit number)

60750254661045926577…86143911202777989119

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.075 × 10¹⁰⁰(101-digit number)

60750254661045926577…86143911202777989121

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

1.215 × 10¹⁰¹(102-digit number)

12150050932209185315…72287822405555978239

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 #2,634,307

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