Block #1,173,563

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 7/28/2015, 1:24:05 AM · Difficulty 10.9376 · 5,653,592 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ec1e8689ac285b2018a85a6b973da4d3f43a9e0153b40c67cd0c1cbc71bbdcee

View on Chainz ↗

Height

#1,173,563

Difficulty

10.937639

Transactions

Size

1.04 KB

Version

Bits

0af00921

Nonce

215,519,895

Timestamp

7/28/2015, 1:24:05 AM

Confirmations

5,653,592

Mined by

⛏️ P2SHARuxPmWhdwPLzrhJtbPWs2rhUf8RQJFcAT

Merkle Root

78925c96473ce9cba003c4ee8a13df8ec970d5ca4dd0537b54d8919c624dbbf3

Transactions (4)

Coinbase6d8eab7053d3c1…babc275c79786a

1 in → 1 out8.3800 XPM110 B

ARuxPmWh…8RQJFcAT

d3fcf777dcca06…348343fe1419a4

1 in → 3 out37.1535 XPM260 B

AaX3taT3…GoQvppAr AR6qgsuL…x1tjMz93 AKsebF9o…26T4a6vn

235558d4bf8f21…da8dd7b62d1936

1 in → 2 out4.4048 XPM227 B

AMetn7Q7…3N4YYF79 AQT8fKCX…Skpqyby4

648790c6fa4937…53f38063469d76

2 in → 2 out5.1135 XPM374 B

AdXCBzey…AhAQpkvh ALSQgVuj…7t2yUBd3

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.

2.234 × 10⁹⁶(97-digit number)

22343858275988126839…83106730951850911999

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

2.234 × 10⁹⁶(97-digit number)

22343858275988126839…83106730951850911999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.234 × 10⁹⁶(97-digit number)

22343858275988126839…83106730951850912001

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

4.468 × 10⁹⁶(97-digit number)

44687716551976253679…66213461903701823999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.468 × 10⁹⁶(97-digit number)

44687716551976253679…66213461903701824001

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

8.937 × 10⁹⁶(97-digit number)

89375433103952507358…32426923807403647999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.937 × 10⁹⁶(97-digit number)

89375433103952507358…32426923807403648001

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

1.787 × 10⁹⁷(98-digit number)

17875086620790501471…64853847614807295999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.787 × 10⁹⁷(98-digit number)

17875086620790501471…64853847614807296001

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

3.575 × 10⁹⁷(98-digit number)

35750173241581002943…29707695229614591999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.575 × 10⁹⁷(98-digit number)

35750173241581002943…29707695229614592001

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 #1,173,563

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