Block #1,000,797

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 4/3/2015, 10:59:02 AM · Difficulty 10.7725 · 5,809,171 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

30178442bd7000580e2b4dabfa023d529eb36ab184f806cd5b4757a0248e2f0e

View on Chainz ↗

Height

#1,000,797

Difficulty

10.772536

Transactions

Size

1.23 KB

Version

Bits

0ac5c4f1

Nonce

1,113,013,283

Timestamp

4/3/2015, 10:59:02 AM

Confirmations

5,809,171

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

d06903bf41f0e7ca7234e2ca4da03a8276090037463f5363a68ee2c54d206117

Transactions (5)

Coinbase72a4f796dc6e15…ab1c6334bbcbac

1 in → 1 out8.6400 XPM116 B

ANSXnLY2…Sd25TjkD

ff25e2c6b26bf6…747e71a09690f7

1 in → 2 out3715.2800 XPM226 B

AY3kst4r…moW3b8ht AGovNBB8…H47jW2YX

f1e17e24df500a…9225c276debca5

2 in → 2 out12.6169 XPM374 B

AbNekQcS…a1edoJoh AJHjTeok…D4NxWi6b

dbd04a8186e8dd…48794c0849f337

1 in → 2 out329.1000 XPM225 B

AUxG8S5r…WWDCiDNH AVocxphT…84Z5jD5j

11d512b18aef32…16e621d46a318d

1 in → 2 out6.7746 XPM226 B

ARJaZD1K…fUngDbaV AY8BF41J…2oiYsnMQ

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.

2.500 × 10⁹⁶(97-digit number)

25003493480881569673…67829720426501898239

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

2.500 × 10⁹⁶(97-digit number)

25003493480881569673…67829720426501898239

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.500 × 10⁹⁶(97-digit number)

25003493480881569673…67829720426501898241

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

5.000 × 10⁹⁶(97-digit number)

50006986961763139346…35659440853003796479

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.000 × 10⁹⁶(97-digit number)

50006986961763139346…35659440853003796481

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

1.000 × 10⁹⁷(98-digit number)

10001397392352627869…71318881706007592959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.000 × 10⁹⁷(98-digit number)

10001397392352627869…71318881706007592961

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

2.000 × 10⁹⁷(98-digit number)

20002794784705255738…42637763412015185919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.000 × 10⁹⁷(98-digit number)

20002794784705255738…42637763412015185921

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

4.000 × 10⁹⁷(98-digit number)

40005589569410511476…85275526824030371839

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.000 × 10⁹⁷(98-digit number)

40005589569410511476…85275526824030371841

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

8.001 × 10⁹⁷(98-digit number)

80011179138821022953…70551053648060743679

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 #1,000,797

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