Block #290,252

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 12/2/2013, 2:33:53 PM · Difficulty 9.9891 · 6,552,920 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

1c76d47dfc8d61d159eb6c9bc0853a98699467877da042f05a53ebbd8d49ba3d

View on Chainz ↗

Height

#290,252

Difficulty

9.989103

Transactions

Size

1.15 KB

Version

Bits

09fd35e0

Nonce

108,153

Timestamp

12/2/2013, 2:33:53 PM

Confirmations

6,552,920

Mined by

⛏️ maRLANtRphoJLqybVjdZeDZHTRvte14t25qjTa

Merkle Root

f958d56e02a0084e656f6dbc79038be7f1bd404149099c6ebb203cc562908575

Transactions (1)

Coinbasef958d56e02a008…203cc562908575

1 in → 30 out9.9900 XPM1.06 KB

ANtRphoJ…4t25qjTa AWCkoGXK…zjpfLbCF AJzWx2VD…j4ZSMit5 AUViUkfG…AuFGajHn AdCxxeng…JqmRFhac

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.

4.025 × 10⁹⁴(95-digit number)

40252924714460338696…70041729464416263999

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

4.025 × 10⁹⁴(95-digit number)

40252924714460338696…70041729464416263999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.025 × 10⁹⁴(95-digit number)

40252924714460338696…70041729464416264001

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

8.050 × 10⁹⁴(95-digit number)

80505849428920677393…40083458928832527999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.050 × 10⁹⁴(95-digit number)

80505849428920677393…40083458928832528001

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

1.610 × 10⁹⁵(96-digit number)

16101169885784135478…80166917857665055999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.610 × 10⁹⁵(96-digit number)

16101169885784135478…80166917857665056001

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

3.220 × 10⁹⁵(96-digit number)

32202339771568270957…60333835715330111999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.220 × 10⁹⁵(96-digit number)

32202339771568270957…60333835715330112001

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

6.440 × 10⁹⁵(96-digit number)

64404679543136541914…20667671430660223999

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 #290,252

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