Block #837,724

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 12/3/2014, 2:37:38 AM · Difficulty 10.9754 · 5,986,846 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

4ca2844839c5c68867bc58c71a744b98eed008271e88865fa6f06cf982e03433

View on Chainz ↗

Height

#837,724

Difficulty

10.975393

Transactions

Size

1.51 KB

Version

Bits

0af9b362

Nonce

1,777,610,757

Timestamp

12/3/2014, 2:37:38 AM

Confirmations

5,986,846

Mined by

⛏️ P2SHAGhX6n5UB5zB9VPhCTF2kqnKzhfQ2dSTgh

Merkle Root

1358dec87397c627c7ff1f2c47675cf1b3de513eb2effe09657d55ef1ffb18ad

Transactions (5)

Coinbase6d689f9ffb0825…a04f067d0edc47

1 in → 1 out8.3300 XPM109 B

AGhX6n5U…fQ2dSTgh

21ca9b8c4b2dd3…9973bb876b9e2d

1 in → 2 out8.2700 XPM227 B

ARqLBueC…qBMDoLmm AS3YRPiP…Qo9e36z6

e809c5d68f7ff5…7403da5ff675e6

2 in → 2 out13.2708 XPM373 B

AHRoHf8T…zepLQuFz AUY54LT9…Q8pWMHVG

03c933490c1ca5…3bc83ba1450825

1 in → 2 out7.2191 XPM227 B

AVZwze3C…1DNKwKx6 AKz7vyo4…do6NvkVJ

82cbe05e524293…3c4b884f4b820f

3 in → 2 out0.5793 XPM522 B

AGmxjBLv…h8KodPXh AHRoBSh4…BSVTQ36Q

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.

2.930 × 10⁹⁷(98-digit number)

29305052050365854489…30847770492133703679

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

2.930 × 10⁹⁷(98-digit number)

29305052050365854489…30847770492133703679

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.930 × 10⁹⁷(98-digit number)

29305052050365854489…30847770492133703681

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

5.861 × 10⁹⁷(98-digit number)

58610104100731708978…61695540984267407359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.861 × 10⁹⁷(98-digit number)

58610104100731708978…61695540984267407361

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

1.172 × 10⁹⁸(99-digit number)

11722020820146341795…23391081968534814719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.172 × 10⁹⁸(99-digit number)

11722020820146341795…23391081968534814721

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

2.344 × 10⁹⁸(99-digit number)

23444041640292683591…46782163937069629439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.344 × 10⁹⁸(99-digit number)

23444041640292683591…46782163937069629441

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

4.688 × 10⁹⁸(99-digit number)

46888083280585367183…93564327874139258879

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.688 × 10⁹⁸(99-digit number)

46888083280585367183…93564327874139258881

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

9.377 × 10⁹⁸(99-digit number)

93776166561170734366…87128655748278517759

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 #837,724

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