Block #637,956

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 7/18/2014, 4:20:19 AM · Difficulty 10.9618 · 6,176,276 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f22f8b8f71c295789559023d229c22e7766bbdb26a9b3535dd5ae36f707c628f

View on Chainz ↗

Height

#637,956

Difficulty

10.961779

Transactions

Size

886 B

Version

Bits

0af63729

Nonce

825,089,433

Timestamp

7/18/2014, 4:20:19 AM

Confirmations

6,176,276

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

c9e6a5d7d2c0b76897e5b29d08ff69182e48c25c11e13f644fa2342cb9df2fd0

Transactions (4)

Coinbase5c44dca48be05c…f40cf9d7c48b00

1 in → 1 out8.3400 XPM116 B

ANSXnLY2…Sd25TjkD

eb14b4c540c659…0e9633856099e2

1 in → 2 out8.3000 XPM225 B

AX8C8jEL…2LHxfgFj AZpdkvSw…MADC6brT

96c6f99b0362d3…8bec075268b9d4

1 in → 2 out7.2883 XPM227 B

ARJvt2aL…HuXdT2ta AKBp1zZ5…q1DHcgUx

186e624a4ef23e…c6859a5cb71b33

1 in → 2 out7.2779 XPM227 B

AWEm1NVx…BSyUpTdF AHCyEg8n…5ABXYgJA

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.

1.252 × 10⁹⁸(99-digit number)

12526277147470513983…11443355311871851519

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

1.252 × 10⁹⁸(99-digit number)

12526277147470513983…11443355311871851519

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.252 × 10⁹⁸(99-digit number)

12526277147470513983…11443355311871851521

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

2.505 × 10⁹⁸(99-digit number)

25052554294941027966…22886710623743703039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.505 × 10⁹⁸(99-digit number)

25052554294941027966…22886710623743703041

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

5.010 × 10⁹⁸(99-digit number)

50105108589882055932…45773421247487406079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.010 × 10⁹⁸(99-digit number)

50105108589882055932…45773421247487406081

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

1.002 × 10⁹⁹(100-digit number)

10021021717976411186…91546842494974812159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.002 × 10⁹⁹(100-digit number)

10021021717976411186…91546842494974812161

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

2.004 × 10⁹⁹(100-digit number)

20042043435952822373…83093684989949624319

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.004 × 10⁹⁹(100-digit number)

20042043435952822373…83093684989949624321

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 #637,956

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