Block #289,051

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 12/2/2013, 12:53:09 AM · Difficulty 9.9882 · 6,518,014 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b6e9a357d79a5041e8663d8983e9e7d69ffcf65206abd3d40bd655e758741124

View on Chainz ↗

Height

#289,051

Difficulty

9.988209

Transactions

Size

1.18 KB

Version

Bits

09fcfb44

Nonce

61,367

Timestamp

12/2/2013, 12:53:09 AM

Confirmations

6,518,014

Mined by

⛏️ iaRAcC2zSodXYDeR5UsaoQ7rZcf2ArtWatH79

Merkle Root

a5dece4b1ba6dee35979bf4818ca37b3e0b0fd72c6bbc6c34659132b1d1f387d

Transactions (1)

Coinbasea5dece4b1ba6de…59132b1d1f387d

1 in → 31 out9.9900 XPM1.09 KB

AcC2zSod…rtWatH79 Acs9SHrk…QJSB8SFG ATpxJmjj…cHQBDptz AcjxqNx1…WJFgsivZ AJzWx2VD…j4ZSMit5

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.

3.432 × 10⁹³(94-digit number)

34325579458645439259…63025001341407479099

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

3.432 × 10⁹³(94-digit number)

34325579458645439259…63025001341407479099

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.432 × 10⁹³(94-digit number)

34325579458645439259…63025001341407479101

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

6.865 × 10⁹³(94-digit number)

68651158917290878519…26050002682814958199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.865 × 10⁹³(94-digit number)

68651158917290878519…26050002682814958201

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

1.373 × 10⁹⁴(95-digit number)

13730231783458175703…52100005365629916399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.373 × 10⁹⁴(95-digit number)

13730231783458175703…52100005365629916401

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

2.746 × 10⁹⁴(95-digit number)

27460463566916351407…04200010731259832799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.746 × 10⁹⁴(95-digit number)

27460463566916351407…04200010731259832801

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

5.492 × 10⁹⁴(95-digit number)

54920927133832702815…08400021462519665599

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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 #289,051

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