Block #1,249,143

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 9/23/2015, 6:09:05 AM · Difficulty 10.7640 · 5,567,780 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

973fcc9a5a953e458cbbf1ff3324b8e892710f7c5b83812a840c6eb8840d7ceb

View on Chainz ↗

Height

#1,249,143

Difficulty

10.764014

Transactions

Size

1.21 KB

Version

Bits

0ac3966b

Nonce

124,612,731

Timestamp

9/23/2015, 6:09:05 AM

Confirmations

5,567,780

Mined by

⛏️ P2SHAJCEY9yyy2DERzsA24UUtHTMGPtg97E6zm

Merkle Root

818f8bb8875abb59a946e554f39fb2b2ac73d86afc5ea1df2c5bb743cdbb5ed0

Transactions (3)

Coinbase37caeaf2d18c83…1d9b5140102e3c

1 in → 1 out8.6400 XPM116 B

AJCEY9yy…tg97E6zm

e88fe4b75d3f9e…765b66fea4a955

1 in → 19 out141.3226 XPM803 B

ATxtsKxe…NAXzXXfQ Acf1mUQq…D62UFq8J AY7dbWcX…CgvvkjSs ATJKL49b…tt6c1rdk AFqAiWtG…JNZAjpHt

323f162a4800a1…236cdcbc0dbdde

1 in → 2 out7.5962 XPM227 B

AWehni14…L1m7zv52 AHbL5bTZ…HvcXG7jd

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.

5.865 × 10⁹⁴(95-digit number)

58656856881577075165…38788055339124827939

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

5.865 × 10⁹⁴(95-digit number)

58656856881577075165…38788055339124827939

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.865 × 10⁹⁴(95-digit number)

58656856881577075165…38788055339124827941

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

1.173 × 10⁹⁵(96-digit number)

11731371376315415033…77576110678249655879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.173 × 10⁹⁵(96-digit number)

11731371376315415033…77576110678249655881

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

2.346 × 10⁹⁵(96-digit number)

23462742752630830066…55152221356499311759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.346 × 10⁹⁵(96-digit number)

23462742752630830066…55152221356499311761

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

4.692 × 10⁹⁵(96-digit number)

46925485505261660132…10304442712998623519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.692 × 10⁹⁵(96-digit number)

46925485505261660132…10304442712998623521

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

9.385 × 10⁹⁵(96-digit number)

93850971010523320264…20608885425997247039

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.385 × 10⁹⁵(96-digit number)

93850971010523320264…20608885425997247041

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 #1,249,143

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