Block #141,836

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/30/2013, 2:15:26 PM · Difficulty 9.8353 · 6,657,478 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

12c69b03298c6d410c804cc9d959c286f0131a205896137b0c3212dc01a6f9b9

View on Chainz ↗

Height

#141,836

Difficulty

9.835254

Transactions

Size

527 B

Version

Bits

09d5d33d

Nonce

97,796

Timestamp

8/30/2013, 2:15:26 PM

Confirmations

6,657,478

Mined by

⛏️ P2SHATMkCkc31UdnGjBtRpGhu2LJhRZjWGrhX6

Merkle Root

6df02948d42ac4ef7e9bbf8ac011ae74b2ff5db5297a9e2057871d45df268f18

Transactions (2)

Coinbase038353171dce9c…baa703174991eb

1 in → 1 out10.3300 XPM109 B

ATMkCkc3…ZjWGrhX6

87eb47858e5da2…9665a75223f4eb

1 in → 5 out2.2195 XPM328 B

AYDNrd6B…NZg5yqPk AHoBiNDF…iqqcEYKL ANKZ8GNu…xk4HrFYE AHTWrMn6…GrqT3BJY AcCPSM1m…r1JwWswB

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.

8.483 × 10⁹³(94-digit number)

84836674030465335027…66939191156990507139

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

8.483 × 10⁹³(94-digit number)

84836674030465335027…66939191156990507139

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.483 × 10⁹³(94-digit number)

84836674030465335027…66939191156990507141

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

1.696 × 10⁹⁴(95-digit number)

16967334806093067005…33878382313981014279

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.696 × 10⁹⁴(95-digit number)

16967334806093067005…33878382313981014281

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

3.393 × 10⁹⁴(95-digit number)

33934669612186134011…67756764627962028559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.393 × 10⁹⁴(95-digit number)

33934669612186134011…67756764627962028561

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

6.786 × 10⁹⁴(95-digit number)

67869339224372268022…35513529255924057119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.786 × 10⁹⁴(95-digit number)

67869339224372268022…35513529255924057121

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

1.357 × 10⁹⁵(96-digit number)

13573867844874453604…71027058511848114239

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