Block #291,725

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 12/3/2013, 8:17:34 AM · Difficulty 9.9900 · 6,520,780 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a99816d099662fdfe2bf063ecf181d1859176619b8f10343f3bd89b79f00a32e

View on Chainz ↗

Height

#291,725

Difficulty

9.989999

Transactions

Size

1.51 KB

Version

Bits

09fd7093

Nonce

77,432

Timestamp

12/3/2013, 8:17:34 AM

Confirmations

6,520,780

Mined by

⛏️ P2SHAUKTrcW2zPnkuASbbEbaBZm2g4MU8UrRfR

Merkle Root

0c032998af4c60d3da230874647375657026be3387b965265b77e1271aaf7087

Transactions (5)

Coinbase6833e6d72d746c…eda537872962c4

1 in → 1 out10.0500 XPM109 B

AUKTrcW2…MU8UrRfR

508386b02f4dd6…7379fabd668dc6

1 in → 2 out27291.2982 XPM226 B

Ae3FupYp…tnRuetDU AJo97mSS…RdMWXRRD

6a3cf05f3677cf…95b80dd542f4c3

4 in → 2 out9.7122 XPM668 B

AMPXXFPB…82Pt9TML AYNitiKx…PFGZ6ohD

c9983ce3e3da5a…a1dc2db6a5151e

1 in → 2 out26707.1882 XPM225 B

AZrD88Gw…VfzXw8Ei AeAsLiAt…AU4FRkbm

a14dfa8c3cae28…7b2b939c730501

1 in → 2 out26667.2835 XPM226 B

AJuDUiKC…8KYxH5Ge AYT7LY2t…5Uu3Rq9m

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.

3.945 × 10⁹³(94-digit number)

39453673267807775983…96807104978736062039

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

3.945 × 10⁹³(94-digit number)

39453673267807775983…96807104978736062039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.945 × 10⁹³(94-digit number)

39453673267807775983…96807104978736062041

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

7.890 × 10⁹³(94-digit number)

78907346535615551966…93614209957472124079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.890 × 10⁹³(94-digit number)

78907346535615551966…93614209957472124081

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

1.578 × 10⁹⁴(95-digit number)

15781469307123110393…87228419914944248159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.578 × 10⁹⁴(95-digit number)

15781469307123110393…87228419914944248161

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

3.156 × 10⁹⁴(95-digit number)

31562938614246220786…74456839829888496319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.156 × 10⁹⁴(95-digit number)

31562938614246220786…74456839829888496321

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

6.312 × 10⁹⁴(95-digit number)

63125877228492441573…48913679659776992639

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 #291,725

Cookie Preferences