Block #687,202

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 8/22/2014, 5:35:31 AM · Difficulty 10.9530 · 6,115,471 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d1983c38ecb994e85bafbdd25ccde82d27c4a5518f1db23e88df898b1da29d77

View on Chainz ↗

Height

#687,202

Difficulty

10.953032

Transactions

Size

718 B

Version

Bits

0af3f9eb

Nonce

1,336,461,706

Timestamp

8/22/2014, 5:35:31 AM

Confirmations

6,115,471

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

5d79e22638f9d58cc9ea78d9790ba930c49407eacbd552c3d3cb08eb43201673

Transactions (2)

Coinbaseae7b410bbc356b…120cefda44ea25

1 in → 1 out8.3300 XPM116 B

ANSXnLY2…Sd25TjkD

b2dc6e673e29e4…ec61524e6624d6

2 in → 7 out14.4925 XPM511 B

Ab2TQhM2…MChPbEoL ASc5A66o…rgEAg76F AcNCFuHi…WhvukeCQ AKinBSz6…c5jHh6RZ AJcmFad4…YNAMFS3w

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.

4.422 × 10⁹⁶(97-digit number)

44225872561804334035…00415236498052235519

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

4.422 × 10⁹⁶(97-digit number)

44225872561804334035…00415236498052235519

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.422 × 10⁹⁶(97-digit number)

44225872561804334035…00415236498052235521

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

8.845 × 10⁹⁶(97-digit number)

88451745123608668070…00830472996104471039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.845 × 10⁹⁶(97-digit number)

88451745123608668070…00830472996104471041

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

1.769 × 10⁹⁷(98-digit number)

17690349024721733614…01660945992208942079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.769 × 10⁹⁷(98-digit number)

17690349024721733614…01660945992208942081

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

3.538 × 10⁹⁷(98-digit number)

35380698049443467228…03321891984417884159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.538 × 10⁹⁷(98-digit number)

35380698049443467228…03321891984417884161

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

7.076 × 10⁹⁷(98-digit number)

70761396098886934456…06643783968835768319

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.076 × 10⁹⁷(98-digit number)

70761396098886934456…06643783968835768321

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