Block #436,989

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/9/2014, 11:46:42 PM · Difficulty 10.3582 · 6,389,125 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e6b8c76b61a38360470cd4e3d428e3646a42f7947d3acd2dbd404acff7b6f22a

View on Chainz ↗

Height

#436,989

Difficulty

10.358175

Transactions

Size

1.01 KB

Version

Bits

0a5bb153

Nonce

88,591

Timestamp

3/9/2014, 11:46:42 PM

Confirmations

6,389,125

Mined by

⛏️ aS#5ANNg88pGRQwFs2RfTXspDobTEJppn21sTe

Merkle Root

0d7e82625b02ffc374f74687eddfc84fb3065b0c39facd2570561770c50fca15

Transactions (1)

Coinbase0d7e82625b02ff…561770c50fca15

1 in → 26 out9.3100 XPM947 B

ANNg88pG…ppn21sTe Aac9Hjdg…P4ktypc3 AScAzqGc…BZ6tV1vJ AGKhfQo2…h7fBXLX6 ALqxX1WA…hsKjbnXn

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.

4.985 × 10⁹³(94-digit number)

49851054676826881599…11184190140584169599

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

4.985 × 10⁹³(94-digit number)

49851054676826881599…11184190140584169599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.985 × 10⁹³(94-digit number)

49851054676826881599…11184190140584169601

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

9.970 × 10⁹³(94-digit number)

99702109353653763198…22368380281168339199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.970 × 10⁹³(94-digit number)

99702109353653763198…22368380281168339201

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

1.994 × 10⁹⁴(95-digit number)

19940421870730752639…44736760562336678399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.994 × 10⁹⁴(95-digit number)

19940421870730752639…44736760562336678401

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

3.988 × 10⁹⁴(95-digit number)

39880843741461505279…89473521124673356799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.988 × 10⁹⁴(95-digit number)

39880843741461505279…89473521124673356801

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

7.976 × 10⁹⁴(95-digit number)

79761687482923010559…78947042249346713599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.976 × 10⁹⁴(95-digit number)

79761687482923010559…78947042249346713601

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 #436,989

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