Block #1,211,733

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 8/28/2015, 10:12:53 AM · Difficulty 10.7526 · 5,631,085 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ee5525247834c1abd8bf96491833aa2d5d1762b6ad4869a7573f74a3f0ce87f5

View on Chainz ↗

Height

#1,211,733

Difficulty

10.752566

Transactions

Size

657 B

Version

Bits

0ac0a832

Nonce

719,102,914

Timestamp

8/28/2015, 10:12:53 AM

Confirmations

5,631,085

Mined by

⛏️ P2SHAJCEY9yyy2DERzsA24UUtHTMGPtg97E6zm

Merkle Root

05ac4b1335dd51db17deadeeced87800627e66967126ae84e2da45ed526ea79e

Transactions (3)

Coinbasec0c048b3385584…90b65b8360d1ef

1 in → 1 out8.6600 XPM116 B

AJCEY9yy…tg97E6zm

0cc0d53c988d23…303758e6ae5cee

1 in → 2 out8.5400 XPM225 B

Aa4PtTwK…H3ppZFzk AWWmzMcR…HTXAERqq

b37b227ac0269a…cdb884d7e785d6

1 in → 2 out1.3761 XPM225 B

AXWveKZz…t4DZJK4K Ad8DTffx…q57AovwF

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.

8.170 × 10⁹⁶(97-digit number)

81702305867941234313…27446553286374975999

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

8.170 × 10⁹⁶(97-digit number)

81702305867941234313…27446553286374975999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.170 × 10⁹⁶(97-digit number)

81702305867941234313…27446553286374976001

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

1.634 × 10⁹⁷(98-digit number)

16340461173588246862…54893106572749951999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.634 × 10⁹⁷(98-digit number)

16340461173588246862…54893106572749952001

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

3.268 × 10⁹⁷(98-digit number)

32680922347176493725…09786213145499903999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.268 × 10⁹⁷(98-digit number)

32680922347176493725…09786213145499904001

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

6.536 × 10⁹⁷(98-digit number)

65361844694352987450…19572426290999807999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.536 × 10⁹⁷(98-digit number)

65361844694352987450…19572426290999808001

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

1.307 × 10⁹⁸(99-digit number)

13072368938870597490…39144852581999615999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.307 × 10⁹⁸(99-digit number)

13072368938870597490…39144852581999616001

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 #1,211,733

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