Block #502,708

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/20/2014, 2:49:26 PM · Difficulty 10.8073 · 6,307,356 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

17e6c5f0e62efc73232182c171b2899ecfd5183e38db3824d327a8af65de82f3

View on Chainz ↗

Height

#502,708

Difficulty

10.807319

Transactions

Size

699 B

Version

Bits

0aceac70

Nonce

339,858,117

Timestamp

4/20/2014, 2:49:26 PM

Confirmations

6,307,356

Mined by

⛏️ QAeX2hokFQpmApFfNcLFPn3VUNCDqikhfHW

Merkle Root

f91e83a4e88d8afa91a9667db514b9a12f0bc9072244e2242b82a1ea86161ba2

Transactions (1)

Coinbasef91e83a4e88d8a…82a1ea86161ba2

1 in → 16 out8.5500 XPM607 B

AeX2hokF…DqikhfHW Aa2Amg89…4rjYrsPZ AREQGaCC…V47D9Shh AMVf7Jrg…xd5AVR7C AGz9gyZW…bo8NYQpw

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.

1.214 × 10⁹⁹(100-digit number)

12143996034429223774…36896982973142318079

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

1.214 × 10⁹⁹(100-digit number)

12143996034429223774…36896982973142318079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.214 × 10⁹⁹(100-digit number)

12143996034429223774…36896982973142318081

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

2.428 × 10⁹⁹(100-digit number)

24287992068858447548…73793965946284636159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.428 × 10⁹⁹(100-digit number)

24287992068858447548…73793965946284636161

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

4.857 × 10⁹⁹(100-digit number)

48575984137716895096…47587931892569272319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.857 × 10⁹⁹(100-digit number)

48575984137716895096…47587931892569272321

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

9.715 × 10⁹⁹(100-digit number)

97151968275433790192…95175863785138544639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.715 × 10⁹⁹(100-digit number)

97151968275433790192…95175863785138544641

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

1.943 × 10¹⁰⁰(101-digit number)

19430393655086758038…90351727570277089279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.943 × 10¹⁰⁰(101-digit number)

19430393655086758038…90351727570277089281

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 #502,708

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