Block #502,973

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/20/2014, 6:48:58 PM · Difficulty 10.8083 · 6,311,839 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

54a42f115297a6edbe45caedf1ab9cadec8d204affa0c97f244f17eaf883b2e0

View on Chainz ↗

Height

#502,973

Difficulty

10.808291

Transactions

Size

885 B

Version

Bits

0aceec24

Nonce

160,935,038

Timestamp

4/20/2014, 6:48:58 PM

Confirmations

6,311,839

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

39b801a1630632486eb5e46d20951c302b42ffc897ecf032d6a136b74d3d1690

Transactions (4)

Coinbase2d3fbe854e34fa…2fa4a3afd0e24a

1 in → 1 out8.5800 XPM116 B

AbwWkWZt…kawDhufa

7f60cff2c0941b…3717d07c7928f6

1 in → 2 out8.5600 XPM227 B

AG8u7ddV…cU5QJSqk Ad1w4bGz…pbJCMd38

f4e2335bcd8293…f08a2eef1536b6

1 in → 2 out7.5403 XPM225 B

AdPna6MP…Nma5bYdx AdqHUiDx…SbeCKBnM

15abe4741c42f7…162928447053f9

1 in → 2 out5.9963 XPM226 B

ASmmxshp…WsUe1AmD AXLffwxx…zkHEyYdn

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.

9.491 × 10⁹⁶(97-digit number)

94918889606976903947…58904643933572010779

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

9.491 × 10⁹⁶(97-digit number)

94918889606976903947…58904643933572010779

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.491 × 10⁹⁶(97-digit number)

94918889606976903947…58904643933572010781

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

1.898 × 10⁹⁷(98-digit number)

18983777921395380789…17809287867144021559

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.898 × 10⁹⁷(98-digit number)

18983777921395380789…17809287867144021561

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

3.796 × 10⁹⁷(98-digit number)

37967555842790761579…35618575734288043119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.796 × 10⁹⁷(98-digit number)

37967555842790761579…35618575734288043121

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

7.593 × 10⁹⁷(98-digit number)

75935111685581523158…71237151468576086239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.593 × 10⁹⁷(98-digit number)

75935111685581523158…71237151468576086241

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

1.518 × 10⁹⁸(99-digit number)

15187022337116304631…42474302937152172479

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.518 × 10⁹⁸(99-digit number)

15187022337116304631…42474302937152172481

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 #502,973

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