Block #772,839

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 10/17/2014, 3:11:39 PM · Difficulty 10.9821 · 6,035,491 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

100efe1e7defd4f98722937af1d558f89b5c0528e298bb133d578f612458d56c

View on Chainz ↗

Height

#772,839

Difficulty

10.982079

Transactions

Size

2.74 KB

Version

Bits

0afb6988

Nonce

651,575,990

Timestamp

10/17/2014, 3:11:39 PM

Confirmations

6,035,491

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

6b3e0a56cb3deb8e2885994e45f208a4d1be51d110c88e92fdd1db98fd69d476

Transactions (4)

Coinbased5692d20a8edc3…e79366118a96f7

1 in → 1 out8.3300 XPM116 B

ANSXnLY2…Sd25TjkD

91304f9825452a…f74021f3263e74

13 in → 2 out101.1748 XPM1.95 KB

APPBcNJi…a8d4Pbip AL7HTuMs…HbLQf7Ue

cfa260fa9354ce…b5467459032f5d

2 in → 2 out11.0490 XPM372 B

AbcdY8zJ…V4YUzF9v ARo6a9MV…VSnEwFef

69f2d0e39d896d…ffaabae8947054

1 in → 2 out6.4414 XPM227 B

AJNGwtao…9ctfATyk AVZwze3C…1DNKwKx6

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.

2.501 × 10⁹⁸(99-digit number)

25016883679861510336…37727068506691174399

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

2.501 × 10⁹⁸(99-digit number)

25016883679861510336…37727068506691174399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.501 × 10⁹⁸(99-digit number)

25016883679861510336…37727068506691174401

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

5.003 × 10⁹⁸(99-digit number)

50033767359723020673…75454137013382348799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.003 × 10⁹⁸(99-digit number)

50033767359723020673…75454137013382348801

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

1.000 × 10⁹⁹(100-digit number)

10006753471944604134…50908274026764697599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.000 × 10⁹⁹(100-digit number)

10006753471944604134…50908274026764697601

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

2.001 × 10⁹⁹(100-digit number)

20013506943889208269…01816548053529395199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.001 × 10⁹⁹(100-digit number)

20013506943889208269…01816548053529395201

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

4.002 × 10⁹⁹(100-digit number)

40027013887778416539…03633096107058790399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.002 × 10⁹⁹(100-digit number)

40027013887778416539…03633096107058790401

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

8.005 × 10⁹⁹(100-digit number)

80054027775556833078…07266192214117580799

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 #772,839

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