Block #321,531

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/20/2013, 9:24:28 AM · Difficulty 10.1907 · 6,474,906 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

feb9c9d438fc70f86675d304f89f123679d2702bb8c52cecd99e2de1f87bf531

View on Chainz ↗

Height

#321,531

Difficulty

10.190706

Transactions

Size

2.25 KB

Version

Bits

0a30d21b

Nonce

35,234

Timestamp

12/20/2013, 9:24:28 AM

Confirmations

6,474,906

Mined by

⛏️ aRANEZwy9tw1DgYw4uGbmja8PNbrE1uf5dKY

Merkle Root

119b772b3fd829ec7278ec257a0fd118f968b51252061eed102d9f7b4b97a529

Transactions (4)

Coinbasec8b65c7dd58941…ecca02d61c0b95

1 in → 1 out9.6100 XPM97 B

ANEZwy9t…E1uf5dKY

093c7599f8db12…2ebb5818cb3c65

11 in → 1 out3.4639 XPM1.63 KB

AP3ojtPV…2kXNSjcE

c9874faee0eb5b…af27f5d1e1a5c7

1 in → 2 out4.5227 XPM226 B

ALQzenxP…2ww16iJD AKWS5T9j…u9q9Z7Zd

c4a135fbf3ac3a…8b30c09723ca28

1 in → 2 out2.2998 XPM225 B

AHY36K53…KaMeAFK5 AbSPQEE7…iMiWQPpc

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.

2.568 × 10⁹⁴(95-digit number)

25688911694238032622…76777368711351982079

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

2.568 × 10⁹⁴(95-digit number)

25688911694238032622…76777368711351982079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.568 × 10⁹⁴(95-digit number)

25688911694238032622…76777368711351982081

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

5.137 × 10⁹⁴(95-digit number)

51377823388476065244…53554737422703964159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.137 × 10⁹⁴(95-digit number)

51377823388476065244…53554737422703964161

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

1.027 × 10⁹⁵(96-digit number)

10275564677695213048…07109474845407928319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.027 × 10⁹⁵(96-digit number)

10275564677695213048…07109474845407928321

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

2.055 × 10⁹⁵(96-digit number)

20551129355390426097…14218949690815856639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.055 × 10⁹⁵(96-digit number)

20551129355390426097…14218949690815856641

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

4.110 × 10⁹⁵(96-digit number)

41102258710780852195…28437899381631713279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.110 × 10⁹⁵(96-digit number)

41102258710780852195…28437899381631713281

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