Block #687,290

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 8/22/2014, 7:06:02 AM · Difficulty 10.9530 · 6,123,051 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

efe85944c7df4f20bc33683f77fca34ac8e32ddc3afb5d9bb78057020ebbb7c3

View on Chainz ↗

Height

#687,290

Difficulty

10.953022

Transactions

Size

1.12 KB

Version

Bits

0af3f942

Nonce

478,948,668

Timestamp

8/22/2014, 7:06:02 AM

Confirmations

6,123,051

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

16a963a85daa308e9b0901649fce1b1493fbca6b7c4d2785202f5b52b81fa4e5

Transactions (4)

Coinbasefe1ff326dd5157…dce123651a2425

1 in → 1 out8.3500 XPM116 B

ANSXnLY2…Sd25TjkD

3819c5357c77be…1242f1bcbf1fa9

1 in → 2 out8.3000 XPM193 B

AeKNrjNj…1NEq95Ta ALeH3dPN…zVgWRzZU

8b0347bf3d6490…fe013f28cec104

3 in → 2 out23.2471 XPM521 B

AXakW2Gz…wPvoRP3m APZZjcPT…mEjtCRTo

797e7af9d81375…da8a8e4e34e0ad

1 in → 2 out7.2620 XPM226 B

ALRwfPbH…GSmYb7Ty AXeRm5HL…gcUDu5dc

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.

9.950 × 10⁹⁶(97-digit number)

99504103410677848786…96248117256171982079

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

9.950 × 10⁹⁶(97-digit number)

99504103410677848786…96248117256171982079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.950 × 10⁹⁶(97-digit number)

99504103410677848786…96248117256171982081

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

1.990 × 10⁹⁷(98-digit number)

19900820682135569757…92496234512343964159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.990 × 10⁹⁷(98-digit number)

19900820682135569757…92496234512343964161

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

3.980 × 10⁹⁷(98-digit number)

39801641364271139514…84992469024687928319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.980 × 10⁹⁷(98-digit number)

39801641364271139514…84992469024687928321

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

7.960 × 10⁹⁷(98-digit number)

79603282728542279028…69984938049375856639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.960 × 10⁹⁷(98-digit number)

79603282728542279028…69984938049375856641

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

1.592 × 10⁹⁸(99-digit number)

15920656545708455805…39969876098751713279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.592 × 10⁹⁸(99-digit number)

15920656545708455805…39969876098751713281

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 #687,290

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