Block #261,924

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/16/2013, 7:48:18 AM · Difficulty 9.9702 · 6,552,119 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

196c6d2aa30bd22909835ee50f705ce124ff5e3ffc1ce4d6abe9edfaf9eb0c29

View on Chainz ↗

Height

#261,924

Difficulty

9.970201

Transactions

Size

21.36 KB

Version

Bits

09f85f1c

Nonce

9,702

Timestamp

11/16/2013, 7:48:18 AM

Confirmations

6,552,119

Mined by

⛏️ P2SHAdGRRh1eP4JFvQMqy7y2pLsryDQmctLb24

Merkle Root

de45a0ef5ec0f4fcec7fdb30aec9ad044b73324de67ff7bdf5ae1fe4c82d90f0

Transactions (3)

Coinbase9d92e155d02f83…aaa51e172fc0c6

1 in → 2 out10.2700 XPM142 B

AdGRRh1e…QmctLb24 AHsw4d6U…EnM8UXNZ

8f464e2a2a0cd2…da01948c4b1029

2 in → 2 out20.0600 XPM373 B

AY1rHXhD…UKxhybo6 ARdEFcSb…mQoSgqJL

fd02efb01fa886…04a7d0316b0570

143 in → 2 out52.0100 XPM20.77 KB

ARVKv5og…ochmCgrB AS6XvSSg…voTjh9Mw

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.

2.028 × 10⁹⁴(95-digit number)

20282622662600428090…06836413089519868039

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

2.028 × 10⁹⁴(95-digit number)

20282622662600428090…06836413089519868039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.028 × 10⁹⁴(95-digit number)

20282622662600428090…06836413089519868041

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

4.056 × 10⁹⁴(95-digit number)

40565245325200856180…13672826179039736079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.056 × 10⁹⁴(95-digit number)

40565245325200856180…13672826179039736081

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

8.113 × 10⁹⁴(95-digit number)

81130490650401712361…27345652358079472159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.113 × 10⁹⁴(95-digit number)

81130490650401712361…27345652358079472161

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

1.622 × 10⁹⁵(96-digit number)

16226098130080342472…54691304716158944319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.622 × 10⁹⁵(96-digit number)

16226098130080342472…54691304716158944321

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

3.245 × 10⁹⁵(96-digit number)

32452196260160684944…09382609432317888639

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.245 × 10⁹⁵(96-digit number)

32452196260160684944…09382609432317888641

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

Block #261,924

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