Block #1,088,983

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 6/4/2015, 3:00:09 AM · Difficulty 10.7458 · 5,717,420 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f22311ed857dfb25f447af27cf3e2fb425469cc0f47c5e5cb989b784d3c26010

View on Chainz ↗

Height

#1,088,983

Difficulty

10.745803

Transactions

Size

83.52 KB

Version

Bits

0abeecee

Nonce

781,298,934

Timestamp

6/4/2015, 3:00:09 AM

Confirmations

5,717,420

Mined by

⛏️ P2SHAV8MXc98ADmQebK3pHtc5ECHvwteYrPbNx

Merkle Root

7d62c2afc76f1bcb36bb0d2bcadf14fbad3656d1dbcd0c9658f023a188e8dc3a

Transactions (2)

Coinbase33e87e56d11ffc…dd3d3836027cfe

1 in → 1 out9.5100 XPM109 B

AV8MXc98…teYrPbNx

64107d7266f9a0…e4437e2e332f2b

576 in → 2 out3000.0100 XPM83.32 KB

AZPRvLoZ…Jdw2MWRN Ae5WFHbn…gBo7rvHr

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.

1.680 × 10⁹⁵(96-digit number)

16801339255861829773…83786055693505287359

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

1.680 × 10⁹⁵(96-digit number)

16801339255861829773…83786055693505287359

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.680 × 10⁹⁵(96-digit number)

16801339255861829773…83786055693505287361

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

3.360 × 10⁹⁵(96-digit number)

33602678511723659546…67572111387010574719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.360 × 10⁹⁵(96-digit number)

33602678511723659546…67572111387010574721

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

6.720 × 10⁹⁵(96-digit number)

67205357023447319093…35144222774021149439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.720 × 10⁹⁵(96-digit number)

67205357023447319093…35144222774021149441

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

1.344 × 10⁹⁶(97-digit number)

13441071404689463818…70288445548042298879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.344 × 10⁹⁶(97-digit number)

13441071404689463818…70288445548042298881

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

2.688 × 10⁹⁶(97-digit number)

26882142809378927637…40576891096084597759

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.688 × 10⁹⁶(97-digit number)

26882142809378927637…40576891096084597761

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 #1,088,983

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