Block #842,528

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 12/6/2014, 5:08:26 PM · Difficulty 10.9736 · 6,000,686 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6bb179ec48122f8bc2759aa888f243702bfeabdcd521c10d57545a5bb4e34a41

View on Chainz ↗

Height

#842,528

Difficulty

10.973582

Transactions

Size

432 B

Version

Bits

0af93caf

Nonce

262,801,116

Timestamp

12/6/2014, 5:08:26 PM

Confirmations

6,000,686

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

cb6ddf8e470299c9cbb9e4852eb41023031fa79aa5fe3af434556169b8475a6c

Transactions (2)

Coinbasefa8476a9a34661…fb37fb8901f442

1 in → 1 out8.3050 XPM116 B

ANSXnLY2…Sd25TjkD

40b3e0eb06e9b8…50d0f09ff2a514

1 in → 2 out2.4068 XPM226 B

AdCLAAPp…ZQS5u867 ALGRFAYr…bdySZ8Jm

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.

3.776 × 10⁹⁵(96-digit number)

37762428175094074527…58075813125703349759

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

3.776 × 10⁹⁵(96-digit number)

37762428175094074527…58075813125703349759

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.776 × 10⁹⁵(96-digit number)

37762428175094074527…58075813125703349761

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

7.552 × 10⁹⁵(96-digit number)

75524856350188149054…16151626251406699519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.552 × 10⁹⁵(96-digit number)

75524856350188149054…16151626251406699521

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

1.510 × 10⁹⁶(97-digit number)

15104971270037629810…32303252502813399039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.510 × 10⁹⁶(97-digit number)

15104971270037629810…32303252502813399041

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

3.020 × 10⁹⁶(97-digit number)

30209942540075259621…64606505005626798079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.020 × 10⁹⁶(97-digit number)

30209942540075259621…64606505005626798081

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

6.041 × 10⁹⁶(97-digit number)

60419885080150519243…29213010011253596159

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.041 × 10⁹⁶(97-digit number)

60419885080150519243…29213010011253596161

Verify on FactorDB ↗Wolfram Alpha ↗

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

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

1.208 × 10⁹⁷(98-digit number)

12083977016030103848…58426020022507192319

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 #842,528

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