Block #635,694

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 7/16/2014, 9:50:04 AM · Difficulty 10.9638 · 6,171,655 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

9829677c703adaf175360ef22ab598cf1e790e46e28cf2c092ee456cf803492c

View on Chainz ↗

Height

#635,694

Difficulty

10.963846

Transactions

Size

1.01 KB

Version

Bits

0af6be9b

Nonce

238,489,107

Timestamp

7/16/2014, 9:50:04 AM

Confirmations

6,171,655

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

fb7eb6727d6c6ecaf58ee2d69eb45bc77d5626585d2c1e559204adc6dcf702f4

Transactions (4)

Coinbase2ef5f8b5e656b2…7ea20919e9cb13

1 in → 1 out8.3400 XPM116 B

ANSXnLY2…Sd25TjkD

41b67d393caf78…2afdb284813fed

2 in → 2 out10.3479 XPM374 B

AcpvpZmH…saT35W1P AeYL6rah…F2TRTpRa

4f77cbf5fd20f3…5e3069226e3857

1 in → 2 out1.1950 XPM226 B

AUx1NT3y…jwLBAmsf AL1fNBDk…WL6sUwM8

621f27c550e5fb…0678f05e4935b5

1 in → 2 out1.0951 XPM227 B

ATPNVTZF…yexnRmNw ASuke7K9…zNKGENjy

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.

5.855 × 10⁹⁷(98-digit number)

58555114560676574614…94615046129135911679

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

5.855 × 10⁹⁷(98-digit number)

58555114560676574614…94615046129135911679

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.855 × 10⁹⁷(98-digit number)

58555114560676574614…94615046129135911681

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

1.171 × 10⁹⁸(99-digit number)

11711022912135314922…89230092258271823359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.171 × 10⁹⁸(99-digit number)

11711022912135314922…89230092258271823361

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

2.342 × 10⁹⁸(99-digit number)

23422045824270629845…78460184516543646719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.342 × 10⁹⁸(99-digit number)

23422045824270629845…78460184516543646721

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

4.684 × 10⁹⁸(99-digit number)

46844091648541259691…56920369033087293439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.684 × 10⁹⁸(99-digit number)

46844091648541259691…56920369033087293441

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

9.368 × 10⁹⁸(99-digit number)

93688183297082519383…13840738066174586879

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.368 × 10⁹⁸(99-digit number)

93688183297082519383…13840738066174586881

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 #635,694

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