Block #591,856

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 6/17/2014, 9:36:15 AM · Difficulty 10.9440 · 6,217,766 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2db094828ab7bc81cd446467b86e2bb5511515b8cf03941aad224c286002173b

View on Chainz ↗

Height

#591,856

Difficulty

10.944030

Transactions

Size

1.01 KB

Version

Bits

0af1abeb

Nonce

21,005

Timestamp

6/17/2014, 9:36:15 AM

Confirmations

6,217,766

Mined by

⛏️ aSBAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

b0eee1e26062ba73a68efffd56c2803697e1e2875d8f6739b9af0e100584210e

Transactions (2)

Coinbase0af13d96b01081…06857527dff64f

1 in → 15 out8.3400 XPM573 B

AQvZBsUo…hppgRZTJ AJzWx2VD…j4ZSMit5 AQv2iMwd…EFna22ee AJtNW28X…Syb4Ph5j AQyr8Lw3…hs4nt3Pn

dae7a81a025bba…90f8c0e8bcfcd6

2 in → 2 out10.5105 XPM373 B

AcXb9hww…EZDriT3f Ac7NL9p4…PuquXQYN

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.

1.430 × 10⁹¹(92-digit number)

14306345708062419430…51914775947830174599

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

1.430 × 10⁹¹(92-digit number)

14306345708062419430…51914775947830174599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.430 × 10⁹¹(92-digit number)

14306345708062419430…51914775947830174601

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

2.861 × 10⁹¹(92-digit number)

28612691416124838860…03829551895660349199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.861 × 10⁹¹(92-digit number)

28612691416124838860…03829551895660349201

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

5.722 × 10⁹¹(92-digit number)

57225382832249677720…07659103791320698399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.722 × 10⁹¹(92-digit number)

57225382832249677720…07659103791320698401

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

1.144 × 10⁹²(93-digit number)

11445076566449935544…15318207582641396799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.144 × 10⁹²(93-digit number)

11445076566449935544…15318207582641396801

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

2.289 × 10⁹²(93-digit number)

22890153132899871088…30636415165282793599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.289 × 10⁹²(93-digit number)

22890153132899871088…30636415165282793601

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 #591,856

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