Block #1,082,667

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/30/2015, 10:07:56 AM · Difficulty 10.7676 · 5,725,213 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

102c97795ab8d7695dd204f3ece12fea75d047fec3628cd72bcb6ebc406aedd4

View on Chainz ↗

Height

#1,082,667

Difficulty

10.767550

Transactions

Size

807 B

Version

Bits

0ac47e30

Nonce

374,570,580

Timestamp

5/30/2015, 10:07:56 AM

Confirmations

5,725,213

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

82c6615afea5859f8d8ac07c075846497393686cc148a50d7395eacac7d04bc3

Transactions (3)

Coinbase57ea32b1a49fb4…a622f1f09387dc

1 in → 1 out8.6300 XPM116 B

ANSXnLY2…Sd25TjkD

f4d2e11c07fe14…b2275aaa587979

2 in → 2 out11.6009 XPM373 B

AZ22hQZu…tRBv56g5 AKTd6ocn…Ewwo3nj2

f23ec98eaa7ac2…5deb9bee069c9a

1 in → 2 out3.5721 XPM227 B

ARDTuBCY…TKZv3MBG AH9HenSr…7F72AXru

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.

1.985 × 10⁹⁶(97-digit number)

19855110019706925920…61240831382171394239

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

1.985 × 10⁹⁶(97-digit number)

19855110019706925920…61240831382171394239

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.985 × 10⁹⁶(97-digit number)

19855110019706925920…61240831382171394241

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

3.971 × 10⁹⁶(97-digit number)

39710220039413851841…22481662764342788479

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.971 × 10⁹⁶(97-digit number)

39710220039413851841…22481662764342788481

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

7.942 × 10⁹⁶(97-digit number)

79420440078827703682…44963325528685576959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.942 × 10⁹⁶(97-digit number)

79420440078827703682…44963325528685576961

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

1.588 × 10⁹⁷(98-digit number)

15884088015765540736…89926651057371153919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.588 × 10⁹⁷(98-digit number)

15884088015765540736…89926651057371153921

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

3.176 × 10⁹⁷(98-digit number)

31768176031531081473…79853302114742307839

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.176 × 10⁹⁷(98-digit number)

31768176031531081473…79853302114742307841

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 #1,082,667

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