Block #493,337

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/15/2014, 3:50:14 PM · Difficulty 10.6980 · 6,309,727 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e9b8622c67363e2f15a2bddee266605c58a0727f1bf324e8e00ea2e1fdca09e1

View on Chainz ↗

Height

#493,337

Difficulty

10.698029

Transactions

Size

971 B

Version

Bits

0ab2b204

Nonce

33,791

Timestamp

4/15/2014, 3:50:14 PM

Confirmations

6,309,727

Mined by

⛏️ uAGz9gyZWgxBxAyVrKrWDzMw21kbo8NYQpw

Merkle Root

ecd839dbd37bea560d9d0226dfeeea92a380e25eab6da9c77821e31c90ca2d34

Transactions (1)

Coinbaseecd839dbd37bea…21e31c90ca2d34

1 in → 24 out8.7200 XPM879 B

AGz9gyZW…bo8NYQpw AMVf7Jrg…xd5AVR7C AdFLJFhb…bsaVkAyh AZ34NcPy…8FPeFjPV AZr7Ptuw…CM4Yw5jq

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.

3.650 × 10⁹⁹(100-digit number)

36505879654232125510…21494122223780382559

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

3.650 × 10⁹⁹(100-digit number)

36505879654232125510…21494122223780382559

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.650 × 10⁹⁹(100-digit number)

36505879654232125510…21494122223780382561

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

7.301 × 10⁹⁹(100-digit number)

73011759308464251020…42988244447560765119

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.301 × 10⁹⁹(100-digit number)

73011759308464251020…42988244447560765121

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

1.460 × 10¹⁰⁰(101-digit number)

14602351861692850204…85976488895121530239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.460 × 10¹⁰⁰(101-digit number)

14602351861692850204…85976488895121530241

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

2.920 × 10¹⁰⁰(101-digit number)

29204703723385700408…71952977790243060479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.920 × 10¹⁰⁰(101-digit number)

29204703723385700408…71952977790243060481

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

5.840 × 10¹⁰⁰(101-digit number)

58409407446771400816…43905955580486120959

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.840 × 10¹⁰⁰(101-digit number)

58409407446771400816…43905955580486120961

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