Block #613,422

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 7/3/2014, 2:35:27 AM · Difficulty 10.9318 · 6,194,798 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

76d5e35b4f2bc83a127952c958c46ac864ce594ff7147d054c49f5ff51ae3554

View on Chainz ↗

Height

#613,422

Difficulty

10.931774

Transactions

Size

1.22 KB

Version

Bits

0aee88c5

Nonce

336,545,621

Timestamp

7/3/2014, 2:35:27 AM

Confirmations

6,194,798

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

7a077e42673893139365954bcbcb7ab06c036ff178f4aea0f1128b983a050aed

Transactions (3)

Coinbase69bfaecb0ecb25…2b07f404110cea

1 in → 1 out8.3700 XPM116 B

ANSXnLY2…Sd25TjkD

28e31ae93b7ef0…5881739651a262

4 in → 1 out4.4128 XPM635 B

AKN4UX7N…18qMKqgj

2a3fe2b4175477…931d882d3691de

2 in → 4 out9.1925 XPM409 B

AcNovFbg…sJ1oLH5E AZoyjqWo…cTWTRwva AeKNrjNj…1NEq95Ta AH1wEe2R…srAfPtHd

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.

7.824 × 10⁹⁸(99-digit number)

78240911442467713870…19785145212440527359

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

7.824 × 10⁹⁸(99-digit number)

78240911442467713870…19785145212440527359

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.824 × 10⁹⁸(99-digit number)

78240911442467713870…19785145212440527361

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

1.564 × 10⁹⁹(100-digit number)

15648182288493542774…39570290424881054719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.564 × 10⁹⁹(100-digit number)

15648182288493542774…39570290424881054721

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

3.129 × 10⁹⁹(100-digit number)

31296364576987085548…79140580849762109439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.129 × 10⁹⁹(100-digit number)

31296364576987085548…79140580849762109441

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

6.259 × 10⁹⁹(100-digit number)

62592729153974171096…58281161699524218879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.259 × 10⁹⁹(100-digit number)

62592729153974171096…58281161699524218881

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

1.251 × 10¹⁰⁰(101-digit number)

12518545830794834219…16562323399048437759

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.251 × 10¹⁰⁰(101-digit number)

12518545830794834219…16562323399048437761

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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 #613,422

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