Block #1,154,842

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 7/14/2015, 11:30:17 AM · Difficulty 10.9466 · 5,672,466 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

7ef4e21f48bd2bf3bc536b0bfad7858ab5a44a703c397b4029405125388a61af

View on Chainz ↗

Height

#1,154,842

Difficulty

10.946630

Transactions

Size

2.87 KB

Version

Bits

0af25657

Nonce

876,024,801

Timestamp

7/14/2015, 11:30:17 AM

Confirmations

5,672,466

Mined by

⛏️ P2SHAdwJngckxeFj33TTKgwgsmoJSaW3LrZeLv

Merkle Root

ef7d4850ca3ad6e431006dce2d8d9a4cbf672b63879dd1584655f255e033d88b

Transactions (2)

Coinbase0bc16510a9ec30…3750f8b8608e0e

1 in → 1 out8.3600 XPM110 B

AdwJngck…W3LrZeLv

a0098966bf9edc…04d3924d7d3406

18 in → 2 out156.0235 XPM2.68 KB

AVrbWLdf…u6iwLxQM AMCcA8Xj…Pb6CL5Sa

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.

2.097 × 10⁹³(94-digit number)

20972684544610939684…09836645159002118399

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

2.097 × 10⁹³(94-digit number)

20972684544610939684…09836645159002118399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.097 × 10⁹³(94-digit number)

20972684544610939684…09836645159002118401

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

4.194 × 10⁹³(94-digit number)

41945369089221879368…19673290318004236799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.194 × 10⁹³(94-digit number)

41945369089221879368…19673290318004236801

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

8.389 × 10⁹³(94-digit number)

83890738178443758736…39346580636008473599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.389 × 10⁹³(94-digit number)

83890738178443758736…39346580636008473601

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

1.677 × 10⁹⁴(95-digit number)

16778147635688751747…78693161272016947199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.677 × 10⁹⁴(95-digit number)

16778147635688751747…78693161272016947201

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

3.355 × 10⁹⁴(95-digit number)

33556295271377503494…57386322544033894399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.355 × 10⁹⁴(95-digit number)

33556295271377503494…57386322544033894401

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 #1,154,842

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