Block #994,569

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 3/28/2015, 7:41:14 PM · Difficulty 10.8433 · 5,830,902 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

79459ece5fd7c6bc3fa1379d60d6a4c3b81536439228cac12d873a7ee9819627

View on Chainz ↗

Height

#994,569

Difficulty

10.843333

Transactions

Size

573 B

Version

Bits

0ad7e4a7

Nonce

108,077,006

Timestamp

3/28/2015, 7:41:14 PM

Confirmations

5,830,902

Mined by

⛏️ P2SHASGr3VmHRh3voR5zFX8diNVPb1i7YthPT7

Merkle Root

ed591c2b9ff0462113689a1161468276269b22ff6feb7e4f92db4f020b0365c4

Transactions (2)

Coinbase7c24aac40d5e2f…cb4f4bc9ca84e5

1 in → 1 out8.5000 XPM109 B

ASGr3VmH…i7YthPT7

4433cdb6138534…ae6398b9ff5f23

2 in → 2 out8.1709 XPM373 B

AQuxwNQx…XzfiDSCq ARFYboDx…3ASsBDJ9

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.

2.394 × 10⁹⁷(98-digit number)

23945562383219744662…94759274505583656959

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

2.394 × 10⁹⁷(98-digit number)

23945562383219744662…94759274505583656959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.394 × 10⁹⁷(98-digit number)

23945562383219744662…94759274505583656961

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

4.789 × 10⁹⁷(98-digit number)

47891124766439489325…89518549011167313919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.789 × 10⁹⁷(98-digit number)

47891124766439489325…89518549011167313921

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

9.578 × 10⁹⁷(98-digit number)

95782249532878978650…79037098022334627839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.578 × 10⁹⁷(98-digit number)

95782249532878978650…79037098022334627841

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

1.915 × 10⁹⁸(99-digit number)

19156449906575795730…58074196044669255679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.915 × 10⁹⁸(99-digit number)

19156449906575795730…58074196044669255681

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

3.831 × 10⁹⁸(99-digit number)

38312899813151591460…16148392089338511359

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.831 × 10⁹⁸(99-digit number)

38312899813151591460…16148392089338511361

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

7.662 × 10⁹⁸(99-digit number)

76625799626303182920…32296784178677022719

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 #994,569

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