Block #701,782

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 8/31/2014, 10:05:26 PM · Difficulty 10.9590 · 6,112,517 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

555c8f57b9d52983dbb25447d517169bd6295b64f27c9d3e52f65816044cedcb

View on Chainz ↗

Height

#701,782

Difficulty

10.959002

Transactions

Size

911 B

Version

Bits

0af5812f

Nonce

1,299,516,893

Timestamp

8/31/2014, 10:05:26 PM

Confirmations

6,112,517

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

f590ad4cb58c9a72a5e2ef3a16aff29edcbd68cf72eb3f04e5083fe7c7579cfd

Transactions (2)

Coinbase59e68a345e2a6a…bcdedcbbed8d5f

1 in → 1 out8.3200 XPM116 B

ANSXnLY2…Sd25TjkD

4d1abb997ada0e…551844dd15db5d

4 in → 3 out4.1831 XPM703 B

AeKNrjNj…1NEq95Ta AYRpw4w5…htLSki3L AGLZ8STd…6UQvoEJw

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.

6.589 × 10⁹⁹(100-digit number)

65895812588401868884…71668172603711487999

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

6.589 × 10⁹⁹(100-digit number)

65895812588401868884…71668172603711487999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.589 × 10⁹⁹(100-digit number)

65895812588401868884…71668172603711488001

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

1.317 × 10¹⁰⁰(101-digit number)

13179162517680373776…43336345207422975999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.317 × 10¹⁰⁰(101-digit number)

13179162517680373776…43336345207422976001

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

2.635 × 10¹⁰⁰(101-digit number)

26358325035360747553…86672690414845951999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.635 × 10¹⁰⁰(101-digit number)

26358325035360747553…86672690414845952001

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

5.271 × 10¹⁰⁰(101-digit number)

52716650070721495107…73345380829691903999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.271 × 10¹⁰⁰(101-digit number)

52716650070721495107…73345380829691904001

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

1.054 × 10¹⁰¹(102-digit number)

10543330014144299021…46690761659383807999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.054 × 10¹⁰¹(102-digit number)

10543330014144299021…46690761659383808001

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

2.108 × 10¹⁰¹(102-digit number)

21086660028288598043…93381523318767615999

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 #701,782

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