Block #669,970

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 8/9/2014, 6:35:12 AM · Difficulty 10.9641 · 6,139,646 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b61244c02840aa099af90190bbcbe3a1a4ef4782e8db2053f1730d77832fd593

View on Chainz ↗

Height

#669,970

Difficulty

10.964110

Transactions

Size

658 B

Version

Bits

0af6cfee

Nonce

2,642,762,126

Timestamp

8/9/2014, 6:35:12 AM

Confirmations

6,139,646

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

b829eb7448639e326c0f2fb4e91a5644fb2853fd92d01dbcce2c10594126d23e

Transactions (3)

Coinbasea5339f3bc7383e…a6f933d9d0a1bb

1 in → 1 out8.3300 XPM116 B

ANSXnLY2…Sd25TjkD

dd65bf8e4d4b2f…1da9c8ffef3c47

1 in → 3 out8.3000 XPM225 B

AeKNrjNj…1NEq95Ta AVMRAzar…3e1KTuWa AUfa5LFJ…C4BhhWGa

9de83fd75121c7…6284ed0b2e20ec

1 in → 2 out6.6544 XPM225 B

AJ3a8ShV…gkjwQkQN ALNQaD7f…2g74yYvV

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.

3.401 × 10⁹⁹(100-digit number)

34012346253983052197…34447006872171642879

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

3.401 × 10⁹⁹(100-digit number)

34012346253983052197…34447006872171642879

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.401 × 10⁹⁹(100-digit number)

34012346253983052197…34447006872171642881

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

6.802 × 10⁹⁹(100-digit number)

68024692507966104395…68894013744343285759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.802 × 10⁹⁹(100-digit number)

68024692507966104395…68894013744343285761

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

1.360 × 10¹⁰⁰(101-digit number)

13604938501593220879…37788027488686571519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.360 × 10¹⁰⁰(101-digit number)

13604938501593220879…37788027488686571521

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

2.720 × 10¹⁰⁰(101-digit number)

27209877003186441758…75576054977373143039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.720 × 10¹⁰⁰(101-digit number)

27209877003186441758…75576054977373143041

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

5.441 × 10¹⁰⁰(101-digit number)

54419754006372883516…51152109954746286079

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.441 × 10¹⁰⁰(101-digit number)

54419754006372883516…51152109954746286081

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

1.088 × 10¹⁰¹(102-digit number)

10883950801274576703…02304219909492572159

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 #669,970

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