Block #585,031

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 6/11/2014, 10:56:11 PM · Difficulty 10.9540 · 6,226,104 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

153fead8c57644676d7edb0a0936eff43a76a930be19408a269d53753aef54f6

View on Chainz ↗

Height

#585,031

Difficulty

10.954032

Transactions

Size

1.80 KB

Version

Bits

0af43b72

Nonce

408,744,506

Timestamp

6/11/2014, 10:56:11 PM

Confirmations

6,226,104

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

8a097dc93b7426916670d1b26d176f81b05060f73a6d2f3d30745624525700ff

Transactions (3)

Coinbase1db658d42d63ec…7d1d267f8d0fbb

1 in → 1 out8.3500 XPM116 B

ANSXnLY2…Sd25TjkD

fe80ecf864b07e…895787cdf00d21

9 in → 2 out144.6799 XPM1.38 KB

AayPMncV…HyCLpuib AUZ3kUe3…Qh4558rj

d8a5e9028dc083…f86fa0868f1c01

1 in → 2 out3.2585 XPM227 B

AGdWVjRk…LFVsqCnK ARvnYp16…2fiH83QN

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.

2.231 × 10⁹⁸(99-digit number)

22313209036114909784…06662904779987373119

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

2.231 × 10⁹⁸(99-digit number)

22313209036114909784…06662904779987373119

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.231 × 10⁹⁸(99-digit number)

22313209036114909784…06662904779987373121

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

4.462 × 10⁹⁸(99-digit number)

44626418072229819569…13325809559974746239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.462 × 10⁹⁸(99-digit number)

44626418072229819569…13325809559974746241

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

8.925 × 10⁹⁸(99-digit number)

89252836144459639139…26651619119949492479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.925 × 10⁹⁸(99-digit number)

89252836144459639139…26651619119949492481

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

1.785 × 10⁹⁹(100-digit number)

17850567228891927827…53303238239898984959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.785 × 10⁹⁹(100-digit number)

17850567228891927827…53303238239898984961

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

3.570 × 10⁹⁹(100-digit number)

35701134457783855655…06606476479797969919

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.570 × 10⁹⁹(100-digit number)

35701134457783855655…06606476479797969921

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 #585,031

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