Block #976,645

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/16/2015, 6:14:27 AM · Difficulty 10.8477 · 5,850,588 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3c88400b427668ef60d435e677019beb7fee1ae677b70a546efb0295c3a48d4d

View on Chainz ↗

Height

#976,645

Difficulty

10.847683

Transactions

Size

3.03 KB

Version

Bits

0ad901bb

Nonce

205,511,117

Timestamp

3/16/2015, 6:14:27 AM

Confirmations

5,850,588

Mined by

⛏️ P2SHAea1rq8WHpuhLq6vcJg1uA15QNr22Uyy6U

Merkle Root

48cd31729fe30e346fb45b4e3fd0d939d723a5da93200b13241bb6adae5ffb7e

Transactions (4)

Coinbased4b3050245fd2e…6ce6b8a3cebf3c

1 in → 1 out8.5300 XPM110 B

Aea1rq8W…r22Uyy6U

7b4ed82ddf0f78…5b56f3d0d103dc

16 in → 2 out134.9296 XPM2.39 KB

AGhXVDpi…Yo6Z7LzC AJg4LkHN…mp6pBP7q

fc9445cd40df87…850ada6a9f6a29

1 in → 2 out7.3633 XPM226 B

Aczu1WTf…yHLDHzX3 AeRaNNK1…cPN5BiRF

e43a1a54be8154…ac13d134628322

1 in → 2 out3.5917 XPM226 B

AWDh2Aht…P35ZUhF1 APHfVo86…ZaZzhZpD

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.

5.685 × 10⁹⁴(95-digit number)

56852073972726543935…75727579571281612799

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

5.685 × 10⁹⁴(95-digit number)

56852073972726543935…75727579571281612799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.685 × 10⁹⁴(95-digit number)

56852073972726543935…75727579571281612801

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

1.137 × 10⁹⁵(96-digit number)

11370414794545308787…51455159142563225599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.137 × 10⁹⁵(96-digit number)

11370414794545308787…51455159142563225601

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

2.274 × 10⁹⁵(96-digit number)

22740829589090617574…02910318285126451199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.274 × 10⁹⁵(96-digit number)

22740829589090617574…02910318285126451201

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

4.548 × 10⁹⁵(96-digit number)

45481659178181235148…05820636570252902399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.548 × 10⁹⁵(96-digit number)

45481659178181235148…05820636570252902401

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

9.096 × 10⁹⁵(96-digit number)

90963318356362470297…11641273140505804799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.096 × 10⁹⁵(96-digit number)

90963318356362470297…11641273140505804801

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 #976,645

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