Block #141,953

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/30/2013, 4:02:55 PM · Difficulty 9.8356 · 6,653,383 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b9453227e304e6fd131ae108814a5bf3bfd5f444560160fe71c8a80ec55a9035

View on Chainz ↗

Height

#141,953

Difficulty

9.835574

Transactions

Size

1.15 KB

Version

Bits

09d5e82e

Nonce

2,374

Timestamp

8/30/2013, 4:02:55 PM

Confirmations

6,653,383

Mined by

⛏️ P2SHAXjr9rkxRCZC5jxDVYUyY67JNp2K8r5i7f

Merkle Root

37eb507ad8edad5783e97cd63be9d0eec2b01c87e4a8ec4b277b5f0c896b290d

Transactions (3)

Coinbase9eca391697f483…0f9394b8712ee7

1 in → 1 out10.3400 XPM109 B

AXjr9rkx…2K8r5i7f

1d4754a1b96b9b…72413c448bd3ad

5 in → 2 out135.1968 XPM823 B

AK3x8dvE…nYbmJccD AUEEzp1B…AyfCNdxm

6c2b35e5b643e3…8c1bcb93bcea94

1 in → 1 out10.3500 XPM158 B

AHjQfvKD…HK5TRF7j

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.

1.911 × 10⁹⁴(95-digit number)

19118457089780715836…17989585127810861999

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

1.911 × 10⁹⁴(95-digit number)

19118457089780715836…17989585127810861999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.911 × 10⁹⁴(95-digit number)

19118457089780715836…17989585127810862001

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

3.823 × 10⁹⁴(95-digit number)

38236914179561431672…35979170255621723999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.823 × 10⁹⁴(95-digit number)

38236914179561431672…35979170255621724001

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

7.647 × 10⁹⁴(95-digit number)

76473828359122863345…71958340511243447999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.647 × 10⁹⁴(95-digit number)

76473828359122863345…71958340511243448001

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

1.529 × 10⁹⁵(96-digit number)

15294765671824572669…43916681022486895999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.529 × 10⁹⁵(96-digit number)

15294765671824572669…43916681022486896001

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

3.058 × 10⁹⁵(96-digit number)

30589531343649145338…87833362044973791999

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