Block #78,750

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/23/2013, 2:14:27 AM · Difficulty 9.2277 · 6,730,536 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

9e525e5fa17e540a17deb1197e2d8df04ff5e4db0378bf5e95649fd1867e9e08

View on Chainz ↗

Height

#78,750

Difficulty

9.227653

Transactions

Size

4.50 KB

Version

Bits

093a4771

Nonce

692

Timestamp

7/23/2013, 2:14:27 AM

Confirmations

6,730,536

Mined by

⛏️ P2SHAUw1hbaeXMZFymZWg2h52gzhrn7L6fpD18

Merkle Root

1c17936dbd376d87f9c2a90a09c9aa7ce40a7d77d3d28c4ae16f801673d6f9c6

Transactions (4)

Coinbase6fe8254d70354c…b9c6d233f58f07

1 in → 1 out11.7900 XPM110 B

AUw1hbae…7L6fpD18

ac6644cb89d142…cb57eac5e5bdc5

2 in → 2 out400.0100 XPM374 B

AWRG57WQ…TggVgSam AJijeTce…FZqaMeBU

e40a76c8d5b083…bb272ca097ccff

1 in → 1 out12.3300 XPM158 B

AMpQJXfH…BPRZ5afz

3fdff9a29a2bb2…2de47c91ba33ea

33 in → 2 out395.3200 XPM3.78 KB

Ab4rdENu…TQCgYmjg ANey87HK…MGUx5bYr

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.

1.578 × 10¹⁰⁵(106-digit number)

15789655029692622940…65593655943100859209

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

1.578 × 10¹⁰⁵(106-digit number)

15789655029692622940…65593655943100859209

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.578 × 10¹⁰⁵(106-digit number)

15789655029692622940…65593655943100859211

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

3.157 × 10¹⁰⁵(106-digit number)

31579310059385245881…31187311886201718419

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.157 × 10¹⁰⁵(106-digit number)

31579310059385245881…31187311886201718421

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

6.315 × 10¹⁰⁵(106-digit number)

63158620118770491763…62374623772403436839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.315 × 10¹⁰⁵(106-digit number)

63158620118770491763…62374623772403436841

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

1.263 × 10¹⁰⁶(107-digit number)

12631724023754098352…24749247544806873679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.263 × 10¹⁰⁶(107-digit number)

12631724023754098352…24749247544806873681

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

2.526 × 10¹⁰⁶(107-digit number)

25263448047508196705…49498495089613747359

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 #78,750

Cookie Preferences