Block #127,567

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 8/21/2013, 2:57:12 PM · Difficulty 9.7841 · 6,687,320 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

30aa03f67f807f289b54f1242be20a8cea46f2facc94aac41fd29be272b8bfb0

View on Chainz ↗

Height

#127,567

Difficulty

9.784062

Transactions

Size

2.54 KB

Version

Bits

09c8b84a

Nonce

46,029

Timestamp

8/21/2013, 2:57:12 PM

Confirmations

6,687,320

Mined by

⛏️ P2SHAQ9FGFAJqsT3PjKGZwrfCCuZRPCAyw6yEq

Merkle Root

697185e2cb1f849df44ca655a00cbc4651095659799278bb9493ab344fc3aa27

Transactions (3)

Coinbase1a41a8dfc32247…32f67f8c8d2893

1 in → 1 out10.4700 XPM109 B

AQ9FGFAJ…CAyw6yEq

86a2d6ea2f9c33…f48563de279193

19 in → 1 out199.1100 XPM2.16 KB

AX7HepGv…Qm28ooHF

484f43454fffda…85219f1493bb6b

1 in → 2 out10.4500 XPM191 B

AXdMPuyd…p5St42C3 AGZvBxxa…shhkwtTn

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.

9.452 × 10⁹⁹(100-digit number)

94526163720502153310…99554809584268851119

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

9.452 × 10⁹⁹(100-digit number)

94526163720502153310…99554809584268851119

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.452 × 10⁹⁹(100-digit number)

94526163720502153310…99554809584268851121

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

1.890 × 10¹⁰⁰(101-digit number)

18905232744100430662…99109619168537702239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.890 × 10¹⁰⁰(101-digit number)

18905232744100430662…99109619168537702241

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

3.781 × 10¹⁰⁰(101-digit number)

37810465488200861324…98219238337075404479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.781 × 10¹⁰⁰(101-digit number)

37810465488200861324…98219238337075404481

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

7.562 × 10¹⁰⁰(101-digit number)

75620930976401722648…96438476674150808959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.562 × 10¹⁰⁰(101-digit number)

75620930976401722648…96438476674150808961

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

1.512 × 10¹⁰¹(102-digit number)

15124186195280344529…92876953348301617919

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.512 × 10¹⁰¹(102-digit number)

15124186195280344529…92876953348301617921

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

3.024 × 10¹⁰¹(102-digit number)

30248372390560689059…85753906696603235839

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 #127,567

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