Block #592,445

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 6/17/2014, 9:27:10 PM · Difficulty 10.9427 · 6,215,351 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

77b5f26a82db530de3412128dcad7e4fbcd6b66cfd954435b086721c0b3902fa

View on Chainz ↗

Height

#592,445

Difficulty

10.942703

Transactions

Size

527 B

Version

Bits

0af154f9

Nonce

463,497

Timestamp

6/17/2014, 9:27:10 PM

Confirmations

6,215,351

Mined by

AQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

e65215f6df4e073c6eb262726988b75c0cf29de96476441f00b1d17bb3ce0828

Transactions (1)

Coinbasee65215f6df4e07…b1d17bb3ce0828

1 in → 11 out8.3400 XPM437 B

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

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.

1.221 × 10⁹⁵(96-digit number)

12211112464142021994…36235692726093649919

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

1.221 × 10⁹⁵(96-digit number)

12211112464142021994…36235692726093649919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.221 × 10⁹⁵(96-digit number)

12211112464142021994…36235692726093649921

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

2.442 × 10⁹⁵(96-digit number)

24422224928284043988…72471385452187299839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.442 × 10⁹⁵(96-digit number)

24422224928284043988…72471385452187299841

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

4.884 × 10⁹⁵(96-digit number)

48844449856568087976…44942770904374599679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.884 × 10⁹⁵(96-digit number)

48844449856568087976…44942770904374599681

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

9.768 × 10⁹⁵(96-digit number)

97688899713136175953…89885541808749199359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.768 × 10⁹⁵(96-digit number)

97688899713136175953…89885541808749199361

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

1.953 × 10⁹⁶(97-digit number)

19537779942627235190…79771083617498398719

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.953 × 10⁹⁶(97-digit number)

19537779942627235190…79771083617498398721

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 #592,445

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