Block #37,960

TWNLength 8★☆☆☆☆

Bi-Twin Chain · Discovered 7/14/2013, 11:22:57 AM · Difficulty 8.1095 · 6,770,361 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

7a0ea204dcf432b2ec8ddba1065981ee62454b3a71b77aba62e33d1b40ad639c

View on Chainz ↗

Height

#37,960

Difficulty

8.109528

Transactions

Size

518 B

Version

Bits

081c0a0f

Nonce

549

Timestamp

7/14/2013, 11:22:57 AM

Confirmations

6,770,361

Mined by

⛏️ P2SHAT356SM4T6yimz2K6Y2kTTvBVB7turso5m

Merkle Root

08aa9cba88aebf7ad9cd260c4bfe9b71896132be214664967efad1ad6daabf78

Transactions (3)

Coinbasebea19f5e849635…e4624dd751f932

1 in → 1 out15.2100 XPM110 B

AT356SM4…7turso5m

39702446903123…d045fd2b14eecd

1 in → 1 out15.6200 XPM158 B

ALkUzjQM…ittmb2bv

6948da51318e65…721b3c23a32bd6

1 in → 1 out15.6200 XPM158 B

AHkEa2Pq…tUzrKxgF

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.

2.007 × 10⁹⁸(99-digit number)

20072470641445055123…05724387948261554999

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

2.007 × 10⁹⁸(99-digit number)

20072470641445055123…05724387948261554999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.007 × 10⁹⁸(99-digit number)

20072470641445055123…05724387948261555001

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

4.014 × 10⁹⁸(99-digit number)

40144941282890110246…11448775896523109999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.014 × 10⁹⁸(99-digit number)

40144941282890110246…11448775896523110001

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

8.028 × 10⁹⁸(99-digit number)

80289882565780220493…22897551793046219999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.028 × 10⁹⁸(99-digit number)

80289882565780220493…22897551793046220001

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

1.605 × 10⁹⁹(100-digit number)

16057976513156044098…45795103586092439999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.605 × 10⁹⁹(100-digit number)

16057976513156044098…45795103586092440001

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 8 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 8

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 #37,960

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