Block #122,973

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/18/2013, 7:14:25 PM · Difficulty 9.7598 · 6,692,873 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c1b3ce9667fa2806e6eab0294f6aac3fbf618184b1e4b426f457d9c8eb3a2201

View on Chainz ↗

Height

#122,973

Difficulty

9.759841

Transactions

Size

2.57 KB

Version

Bits

09c284ec

Nonce

338,965

Timestamp

8/18/2013, 7:14:25 PM

Confirmations

6,692,873

Mined by

⛏️ P2SHAFz7u2qS8oWE6xaxgPhKWKwTURzTPiBUHD

Merkle Root

9a09f46288fafe24ecfe3a80d5f7084ecad5d32db7fe7c1da4406617fcaea3dc

Transactions (2)

Coinbase08bd22df50cd79…7fea01ae4c2e32

1 in → 1 out10.5100 XPM109 B

AFz7u2qS…zTPiBUHD

30bd8570681a64…03ffb0445b1613

20 in → 2 out200.0101 XPM2.37 KB

ATWpCFic…6AT1WprT Adc3z6rn…wymM6aTE

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.

7.362 × 10⁹⁷(98-digit number)

73628352382178471042…23200586072416023799

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

7.362 × 10⁹⁷(98-digit number)

73628352382178471042…23200586072416023799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.362 × 10⁹⁷(98-digit number)

73628352382178471042…23200586072416023801

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

1.472 × 10⁹⁸(99-digit number)

14725670476435694208…46401172144832047599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.472 × 10⁹⁸(99-digit number)

14725670476435694208…46401172144832047601

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

2.945 × 10⁹⁸(99-digit number)

29451340952871388416…92802344289664095199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.945 × 10⁹⁸(99-digit number)

29451340952871388416…92802344289664095201

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

5.890 × 10⁹⁸(99-digit number)

58902681905742776833…85604688579328190399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.890 × 10⁹⁸(99-digit number)

58902681905742776833…85604688579328190401

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

1.178 × 10⁹⁹(100-digit number)

11780536381148555366…71209377158656380799

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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 #122,973

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