Block #636,527

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 7/16/2014, 11:58:25 PM · Difficulty 10.9637 · 6,171,544 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ca7f61151c733cb9611d442ecab1823a0fbedfbb78b65263054c6ef2bb4345b8

View on Chainz ↗

Height

#636,527

Difficulty

10.963737

Transactions

Size

1.80 KB

Version

Bits

0af6b77c

Nonce

433,551,630

Timestamp

7/16/2014, 11:58:25 PM

Confirmations

6,171,544

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

22b23ecad8eb0b0685e02e8945477ecf2b83cb8a1288405373d9b65cfe70fa19

Transactions (3)

Coinbase8dd191cca78028…47f898eadc69d2

1 in → 1 out8.3400 XPM116 B

ANSXnLY2…Sd25TjkD

c34e50e4cf80b5…0d5e0fe60d5417

9 in → 2 out20.2934 XPM1.38 KB

AGkquvq7…XPiNNY6U AXDS5S83…LHa58BH1

ddd779c6b22962…6cac8a524bc93e

1 in → 2 out2.1622 XPM227 B

AekThyRg…BwvL573j ALNQaD7f…2g74yYvV

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.

5.256 × 10⁹⁹(100-digit number)

52569505444291789903…77548565233549311999

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

5.256 × 10⁹⁹(100-digit number)

52569505444291789903…77548565233549311999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.256 × 10⁹⁹(100-digit number)

52569505444291789903…77548565233549312001

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

1.051 × 10¹⁰⁰(101-digit number)

10513901088858357980…55097130467098623999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.051 × 10¹⁰⁰(101-digit number)

10513901088858357980…55097130467098624001

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

2.102 × 10¹⁰⁰(101-digit number)

21027802177716715961…10194260934197247999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.102 × 10¹⁰⁰(101-digit number)

21027802177716715961…10194260934197248001

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

4.205 × 10¹⁰⁰(101-digit number)

42055604355433431922…20388521868394495999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.205 × 10¹⁰⁰(101-digit number)

42055604355433431922…20388521868394496001

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

8.411 × 10¹⁰⁰(101-digit number)

84111208710866863844…40777043736788991999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.411 × 10¹⁰⁰(101-digit number)

84111208710866863844…40777043736788992001

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 #636,527

Cookie Preferences