Block #620,223

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 7/6/2014, 7:12:50 PM · Difficulty 10.9494 · 6,188,346 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e65e26bbddfe537159cde68c3a85221605b838471a6d3afed60f0491bcbb5714

View on Chainz ↗

Height

#620,223

Difficulty

10.949367

Transactions

Size

1.81 KB

Version

Bits

0af309b6

Nonce

1,976,479,435

Timestamp

7/6/2014, 7:12:50 PM

Confirmations

6,188,346

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

a8b8d10aa748f8e26fcd72a8c8ca795ae4044a07638232a8bbdf5f0d57744020

Transactions (5)

Coinbasefa8c0a8e676fb0…0a42810fcee90b

1 in → 1 out8.3700 XPM116 B

ANSXnLY2…Sd25TjkD

777472ea13a1af…dc8bb98afbe255

6 in → 2 out50.0700 XPM966 B

APCYz4Ew…ZdHJqDhg Ab76s4bb…qisi9N3m

99195fe0bcc53a…28fdb31f8f676b

1 in → 2 out6.6375 XPM225 B

AM23VEk3…q622MtoH AZS4jSRE…vJpWBsmJ

9006ff42359285…9676c0e72c87b3

1 in → 2 out6.2925 XPM227 B

AUL2qfqS…38afSsEu AcKerPva…qeeuPChG

222e42e638e063…1ee183624c129a

1 in → 2 out3.0904 XPM227 B

AZY55JsG…1CZ8TYK4 AGzX6zrq…2sUqUFQZ

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.

5.492 × 10⁹⁸(99-digit number)

54922798219528566479…18206461059843624959

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

5.492 × 10⁹⁸(99-digit number)

54922798219528566479…18206461059843624959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.492 × 10⁹⁸(99-digit number)

54922798219528566479…18206461059843624961

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

1.098 × 10⁹⁹(100-digit number)

10984559643905713295…36412922119687249919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.098 × 10⁹⁹(100-digit number)

10984559643905713295…36412922119687249921

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

2.196 × 10⁹⁹(100-digit number)

21969119287811426591…72825844239374499839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.196 × 10⁹⁹(100-digit number)

21969119287811426591…72825844239374499841

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

4.393 × 10⁹⁹(100-digit number)

43938238575622853183…45651688478748999679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.393 × 10⁹⁹(100-digit number)

43938238575622853183…45651688478748999681

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

8.787 × 10⁹⁹(100-digit number)

87876477151245706367…91303376957497999359

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.787 × 10⁹⁹(100-digit number)

87876477151245706367…91303376957497999361

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

1.757 × 10¹⁰⁰(101-digit number)

17575295430249141273…82606753914995998719

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 #620,223

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