Block #589,104

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 6/15/2014, 5:22:17 AM · Difficulty 10.9481 · 6,206,252 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

701238205a48e5a3be59e95f63284e16ac30893c293dd8427f7385daf622c962

View on Chainz ↗

Height

#589,104

Difficulty

10.948051

Transactions

Size

2.67 KB

Version

Bits

0af2b37a

Nonce

2,566,134,292

Timestamp

6/15/2014, 5:22:17 AM

Confirmations

6,206,252

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

00e6613c4d99d51053d7533c087aa209737a2fd387f3c5018688555514ffdf0b

Transactions (5)

Coinbaseff05dd14d1c2b1…b35c44409389e5

1 in → 1 out8.3800 XPM116 B

ANSXnLY2…Sd25TjkD

e37d11d0111a15…3847381b4948b0

11 in → 2 out60.5560 XPM1.67 KB

AW6Cei3u…fGJvgpw8 ARyiKh56…EvMgPXNm

ee97b8921e856c…98b9bdd978ff7e

2 in → 2 out10.5221 XPM374 B

AWZrygnL…61xoXvPo AY4uM53e…yee8uDKH

4cc487c02c5a24…df2497ab6ace05

1 in → 2 out7.2488 XPM225 B

APpP3ChP…b5wSFUFz AcB1Cdou…cFjow1c5

1cc0a482d22c50…edde20a845b3fc

1 in → 2 out3.9832 XPM226 B

AJTsLJ89…rErdMt2e AeGhnUtw…t4YyeP4J

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.

2.511 × 10⁹⁷(98-digit number)

25115555154147158376…66199221881512408799

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

2.511 × 10⁹⁷(98-digit number)

25115555154147158376…66199221881512408799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.511 × 10⁹⁷(98-digit number)

25115555154147158376…66199221881512408801

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

5.023 × 10⁹⁷(98-digit number)

50231110308294316752…32398443763024817599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.023 × 10⁹⁷(98-digit number)

50231110308294316752…32398443763024817601

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

1.004 × 10⁹⁸(99-digit number)

10046222061658863350…64796887526049635199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.004 × 10⁹⁸(99-digit number)

10046222061658863350…64796887526049635201

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

2.009 × 10⁹⁸(99-digit number)

20092444123317726701…29593775052099270399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.009 × 10⁹⁸(99-digit number)

20092444123317726701…29593775052099270401

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

4.018 × 10⁹⁸(99-digit number)

40184888246635453402…59187550104198540799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.018 × 10⁹⁸(99-digit number)

40184888246635453402…59187550104198540801

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