Block #1,487,933

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/7/2016, 9:10:13 PM · Difficulty 10.7166 · 5,326,259 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

1cc61e879ac2a3feb15745b0bca04fd9699046423422ddcb50da84bce21afbc0

View on Chainz ↗

Height

#1,487,933

Difficulty

10.716637

Transactions

Size

1.63 KB

Version

Bits

0ab7758c

Nonce

523,742,454

Timestamp

3/7/2016, 9:10:13 PM

Confirmations

5,326,259

Mined by

⛏️ P2SHAFszcahcAx1RmKTxZPYijRethLVyzoScyX

Merkle Root

52977ba14615a454140b7c92625cc765c784584ab536ab559e5eeacd9d1aa209

Transactions (3)

Coinbase0163f7c0d8a459…69bd8313d2a9e7

1 in → 1 out8.7269 XPM109 B

AFszcahc…VyzoScyX

45284264765be6…4d1d891b643293

1 in → 1 out0.0239 XPM191 B

ANUJpe11…Wc7ycVUW

2df2ea949c2eb8…5d6803e3eb2ce3

1 in → 33 out57.7049 XPM1.25 KB

AFujNYWe…eYMgrthf AHUnFPcc…YB39UjTG AcyWLcPW…MBkw4RHa AHjwfhMe…6kjquBob AZ7bdUiQ…VWjibCPn

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.

7.087 × 10⁹⁴(95-digit number)

70871222474437116237…76779468039116154639

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

7.087 × 10⁹⁴(95-digit number)

70871222474437116237…76779468039116154639

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.087 × 10⁹⁴(95-digit number)

70871222474437116237…76779468039116154641

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

1.417 × 10⁹⁵(96-digit number)

14174244494887423247…53558936078232309279

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.417 × 10⁹⁵(96-digit number)

14174244494887423247…53558936078232309281

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

2.834 × 10⁹⁵(96-digit number)

28348488989774846494…07117872156464618559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.834 × 10⁹⁵(96-digit number)

28348488989774846494…07117872156464618561

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

5.669 × 10⁹⁵(96-digit number)

56696977979549692989…14235744312929237119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.669 × 10⁹⁵(96-digit number)

56696977979549692989…14235744312929237121

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

1.133 × 10⁹⁶(97-digit number)

11339395595909938597…28471488625858474239

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.133 × 10⁹⁶(97-digit number)

11339395595909938597…28471488625858474241

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 #1,487,933

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