Block #1,223,604

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 9/5/2015, 7:52:10 PM · Difficulty 10.7414 · 5,567,400 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

7391009951dbddcd2ed82213b2aebd100f543316363f660d09f8542fbae0ca42

View on Chainz ↗

Height

#1,223,604

Difficulty

10.741448

Transactions

Size

573 B

Version

Bits

0abdcf91

Nonce

947,948,685

Timestamp

9/5/2015, 7:52:10 PM

Confirmations

5,567,400

Merkle Root

8018889242b9d8866270ccdc39ce320c1e3217ba8fa16dcefac64396bd9dd268

Transactions (2)

Coinbasee5d759969df504…6ed66326a8cb44

1 in → 1 out8.6600 XPM109 B

AGHWh1q6…giyUshgm

227f59097dee1a…5118361665b6f7

2 in → 2 out11.6077 XPM374 B

AJRwGPSP…QDRWdi2B AHp5QrYR…drkKxy4y

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.

1.066 × 10⁹⁵(96-digit number)

10660568207676278399…90549002998572026879

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

1.066 × 10⁹⁵(96-digit number)

10660568207676278399…90549002998572026879

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.066 × 10⁹⁵(96-digit number)

10660568207676278399…90549002998572026881

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

2.132 × 10⁹⁵(96-digit number)

21321136415352556799…81098005997144053759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.132 × 10⁹⁵(96-digit number)

21321136415352556799…81098005997144053761

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

4.264 × 10⁹⁵(96-digit number)

42642272830705113599…62196011994288107519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.264 × 10⁹⁵(96-digit number)

42642272830705113599…62196011994288107521

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

8.528 × 10⁹⁵(96-digit number)

85284545661410227199…24392023988576215039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.528 × 10⁹⁵(96-digit number)

85284545661410227199…24392023988576215041

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

1.705 × 10⁹⁶(97-digit number)

17056909132282045439…48784047977152430079

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.705 × 10⁹⁶(97-digit number)

17056909132282045439…48784047977152430081

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

3.411 × 10⁹⁶(97-digit number)

34113818264564090879…97568095954304860159

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