Block #74,745

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/21/2013, 12:41:16 PM · Difficulty 8.9957 · 6,728,702 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

00378f54323737e564f09327e82f2388fe56e873e898bdad948b34da2ccbfb66

View on Chainz ↗

Height

#74,745

Difficulty

8.995703

Transactions

Size

1.22 KB

Version

Bits

08fee668

Nonce

120

Timestamp

7/21/2013, 12:41:16 PM

Confirmations

6,728,702

Mined by

⛏️ P2SHAX5TJE28UFcHEHCUQXe8Ag1tNsuYocNWtF

Merkle Root

d3667a200498468518288876610c35ee7ac672de73c140e6681b69e2cedbcfb4

Transactions (3)

Coinbased67f9886a85bee…c9f548d52be202

1 in → 1 out12.3600 XPM110 B

AX5TJE28…uYocNWtF

90c8428a98ec0d…360e45bc910536

2 in → 2 out99.9474 XPM374 B

AGpBLbTY…XyhUFmrh ARKdaEGA…BQbYGo9W

641a9508ab9750…8c36afc5f0514b

4 in → 2 out49.2889 XPM670 B

AcmAAoxS…6A4y479Q ALxzEmD2…hmsCULKi

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.

3.097 × 10¹⁰¹(102-digit number)

30970717618116082101…79343885101148728709

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

3.097 × 10¹⁰¹(102-digit number)

30970717618116082101…79343885101148728709

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.097 × 10¹⁰¹(102-digit number)

30970717618116082101…79343885101148728711

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

6.194 × 10¹⁰¹(102-digit number)

61941435236232164202…58687770202297457419

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.194 × 10¹⁰¹(102-digit number)

61941435236232164202…58687770202297457421

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

1.238 × 10¹⁰²(103-digit number)

12388287047246432840…17375540404594914839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.238 × 10¹⁰²(103-digit number)

12388287047246432840…17375540404594914841

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

2.477 × 10¹⁰²(103-digit number)

24776574094492865680…34751080809189829679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.477 × 10¹⁰²(103-digit number)

24776574094492865680…34751080809189829681

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

4.955 × 10¹⁰²(103-digit number)

49553148188985731361…69502161618379659359

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