Block #1,251,747

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 9/24/2015, 8:06:57 PM · Difficulty 10.7789 · 5,565,544 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

9ec2973a455b0c3dbee8f5c06ac28d9360668ceb52876fb757521488230fddf7

View on Chainz ↗

Height

#1,251,747

Difficulty

10.778903

Transactions

Size

1.17 KB

Version

Bits

0ac76634

Nonce

1,770,924,871

Timestamp

9/24/2015, 8:06:57 PM

Confirmations

5,565,544

Mined by

⛏️ P2SHAUVgrQgehMixYeDPaM8QPmfiJeJfbxGchT

Merkle Root

604104704548c67ff7246c4bbbba62187ca883dd3c99d05dcde71e689256b6f9

Transactions (3)

Coinbase2622048ba471f1…b29acd1dbf79c8

1 in → 1 out8.6100 XPM110 B

AUVgrQge…JfbxGchT

d425168d0db76b…c3ad1dc9fc4695

1 in → 18 out119.3340 XPM770 B

AZ2Dv6vs…YoKVyFme AS8tXSFT…PVqdRMGe AZbc85DY…rvEMeXki AKvfQFwC…VoCqRW3f AJr2vTeb…C2PTxX5H

4ee2225f1d1eca…cbbedd46f9f99e

1 in → 2 out5.5729 XPM226 B

AcuM7XiJ…5uND8Jce AMiKSgA3…wmV1rwLC

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.

8.569 × 10⁹⁴(95-digit number)

85696261740327575907…53377480728589055199

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

8.569 × 10⁹⁴(95-digit number)

85696261740327575907…53377480728589055199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.569 × 10⁹⁴(95-digit number)

85696261740327575907…53377480728589055201

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

1.713 × 10⁹⁵(96-digit number)

17139252348065515181…06754961457178110399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.713 × 10⁹⁵(96-digit number)

17139252348065515181…06754961457178110401

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

3.427 × 10⁹⁵(96-digit number)

34278504696131030363…13509922914356220799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.427 × 10⁹⁵(96-digit number)

34278504696131030363…13509922914356220801

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

6.855 × 10⁹⁵(96-digit number)

68557009392262060726…27019845828712441599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.855 × 10⁹⁵(96-digit number)

68557009392262060726…27019845828712441601

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

1.371 × 10⁹⁶(97-digit number)

13711401878452412145…54039691657424883199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.371 × 10⁹⁶(97-digit number)

13711401878452412145…54039691657424883201

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 #1,251,747

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