Block #605,006

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 6/28/2014, 5:23:32 AM · Difficulty 10.9099 · 6,221,040 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c5e9e9276313f7550008e0c7dc0b75e547cf3e3461180fc261fb44fc94fb41fa

View on Chainz ↗

Height

#605,006

Difficulty

10.909870

Transactions

Size

1.52 KB

Version

Bits

0ae8ed36

Nonce

136,083,895

Timestamp

6/28/2014, 5:23:32 AM

Confirmations

6,221,040

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

69b5616b701dc63ccf33938362262c9049da801432701b7c14e64ea32d6c556a

Transactions (5)

Coinbase354d0f11759fb1…0a6afbc98857d2

1 in → 1 out8.4300 XPM116 B

ANSXnLY2…Sd25TjkD

5ff4825856cc4c…e4241d21fc8fe9

1 in → 2 out5.1852 XPM226 B

AMMS62VV…LatcTBEd AJJXu42t…MXuyGH1z

80290dcebd351f…2a1eb038bf4c6a

1 in → 2 out3.9577 XPM226 B

AMVPQmEW…XvoLn1a2 AS9ZCvju…bu3NEFwZ

37199e3e5e0b0e…8de4421d8bcc0e

1 in → 2 out5.0125 XPM227 B

AKd3f6Lh…vYfjc19Q Abs1CTRR…uk6ieBYF

9b7d2d06fc540a…982d8153d30820

4 in → 2 out7.0514 XPM671 B

AYVTN5VN…Z4CTaeUB AZS4yuXr…deWqZ51K

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.

5.522 × 10⁹⁹(100-digit number)

55229766996384923182…74414878536745369599

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

5.522 × 10⁹⁹(100-digit number)

55229766996384923182…74414878536745369599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.522 × 10⁹⁹(100-digit number)

55229766996384923182…74414878536745369601

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

1.104 × 10¹⁰⁰(101-digit number)

11045953399276984636…48829757073490739199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.104 × 10¹⁰⁰(101-digit number)

11045953399276984636…48829757073490739201

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

2.209 × 10¹⁰⁰(101-digit number)

22091906798553969273…97659514146981478399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.209 × 10¹⁰⁰(101-digit number)

22091906798553969273…97659514146981478401

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

4.418 × 10¹⁰⁰(101-digit number)

44183813597107938546…95319028293962956799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.418 × 10¹⁰⁰(101-digit number)

44183813597107938546…95319028293962956801

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

8.836 × 10¹⁰⁰(101-digit number)

88367627194215877092…90638056587925913599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.836 × 10¹⁰⁰(101-digit number)

88367627194215877092…90638056587925913601

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 #605,006

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