Block #1,177,407

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 7/30/2015, 7:45:03 PM · Difficulty 10.9360 · 5,639,351 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

852503c433b817052a2408b590ce090d06cc40385c00afa6a5643cdf98cfd043

View on Chainz ↗

Height

#1,177,407

Difficulty

10.936029

Transactions

Size

1.28 KB

Version

Bits

0aef9f9a

Nonce

2,126,842,033

Timestamp

7/30/2015, 7:45:03 PM

Confirmations

5,639,351

Mined by

⛏️ P2SHASoXp2AsQxHaMM6GbHYqBtVE3cedjAmBXG

Merkle Root

0fa345abf5bd7ddd0deaca5da91d93e810e8bed2afcbdf2e82d92e09372baa06

Transactions (2)

Coinbasef9fc98c8dcd26b…ba19a55aba9484

1 in → 1 out8.3700 XPM109 B

ASoXp2As…edjAmBXG

9d7d2b4c438d4e…1c022cbae98c16

7 in → 2 out60.1705 XPM1.09 KB

AZ3B1cCv…MpotD5dU AK9LxQQh…h24pctRm

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.

1.059 × 10⁹⁷(98-digit number)

10591703899756746559…15991003514404782079

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

1.059 × 10⁹⁷(98-digit number)

10591703899756746559…15991003514404782079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.059 × 10⁹⁷(98-digit number)

10591703899756746559…15991003514404782081

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

2.118 × 10⁹⁷(98-digit number)

21183407799513493118…31982007028809564159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.118 × 10⁹⁷(98-digit number)

21183407799513493118…31982007028809564161

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

4.236 × 10⁹⁷(98-digit number)

42366815599026986237…63964014057619128319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.236 × 10⁹⁷(98-digit number)

42366815599026986237…63964014057619128321

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

8.473 × 10⁹⁷(98-digit number)

84733631198053972475…27928028115238256639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.473 × 10⁹⁷(98-digit number)

84733631198053972475…27928028115238256641

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

1.694 × 10⁹⁸(99-digit number)

16946726239610794495…55856056230476513279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.694 × 10⁹⁸(99-digit number)

16946726239610794495…55856056230476513281

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 #1,177,407

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