Block #146,534

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 9/2/2013, 1:51:32 PM · Difficulty 9.8480 · 6,653,824 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f9c94b1e764299ba8e7cc61a0cadb37904cd11d5efce9fa5929b3f43eb49bf07

View on Chainz ↗

Height

#146,534

Difficulty

9.848042

Transactions

Size

649 B

Version

Bits

09d91948

Nonce

62,953

Timestamp

9/2/2013, 1:51:32 PM

Confirmations

6,653,824

Mined by

⛏️ P2SHAYMaGtvfYLa652zDmUi2Bp4ockST8UXmuD

Merkle Root

3d137286ab1f42bf6d6a08cba5608c46498ee7d8419ddedb47eeeb398fcd46d9

Transactions (3)

Coinbase10ccf0af6853d1…38e48a2a4dffc0

1 in → 1 out10.3200 XPM109 B

AYMaGtvf…ST8UXmuD

b3c5e2ee3f25c6…406dfc87858e3f

1 in → 2 out3.2744 XPM225 B

AbjLQB3Y…SXLCXwVY AbqmJmQu…Z2H39LQc

9af6861dd067be…078a6577ba3b7f

1 in → 2 out2.1712 XPM226 B

AVzwxDBw…FEYwsHTn Af6R9E9b…tSYeZAus

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.

1.048 × 10⁹²(93-digit number)

10485034933391041639…13997924038348380919

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

1.048 × 10⁹²(93-digit number)

10485034933391041639…13997924038348380919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.048 × 10⁹²(93-digit number)

10485034933391041639…13997924038348380921

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

2.097 × 10⁹²(93-digit number)

20970069866782083278…27995848076696761839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.097 × 10⁹²(93-digit number)

20970069866782083278…27995848076696761841

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

4.194 × 10⁹²(93-digit number)

41940139733564166556…55991696153393523679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.194 × 10⁹²(93-digit number)

41940139733564166556…55991696153393523681

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

8.388 × 10⁹²(93-digit number)

83880279467128333113…11983392306787047359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.388 × 10⁹²(93-digit number)

83880279467128333113…11983392306787047361

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

1.677 × 10⁹³(94-digit number)

16776055893425666622…23966784613574094719

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.677 × 10⁹³(94-digit number)

16776055893425666622…23966784613574094721

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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