Block #536,327

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/11/2014, 9:01:47 AM · Difficulty 10.9092 · 6,297,528 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

87945551a9442d3f31834b52547e5aebd9b63ab33bd1801842d1939f29b1f4ac

View on Chainz ↗

Height

#536,327

Difficulty

10.909242

Transactions

Size

1.34 KB

Version

Bits

0ae8c411

Nonce

38,258,578

Timestamp

5/11/2014, 9:01:47 AM

Confirmations

6,297,528

Mined by

⛏️ P2SHAWepa96YXDNnEMPiXmYtquwor3NVq6Qk1n

Merkle Root

92b4d5140311c7672cef1655042aa586cafa751e45169e7f2fb0524b95fe9fe2

Transactions (5)

Coinbasef5f29dde95a124…3b0ce040f80c81

1 in → 1 out8.4400 XPM109 B

AWepa96Y…NVq6Qk1n

ae72a2b077e6dd…beb02ed58674f8

3 in → 2 out10.1967 XPM523 B

ALrcMckk…REDxLu7Y AazYJGhE…66XFyGZ2

63acb32cb4d3b6…5c0d175c26b025

1 in → 2 out3.7651 XPM225 B

AR57wig1…YwqXKhMy APxHkbwM…Uw5iSNK6

e565e2c2bf4da4…d6bc57c412afa1

1 in → 1 out0.4500 XPM192 B

Aa9cUEsx…UFEdkErT

e5bfa235ee5b9c…50aca8fff89528

1 in → 2 out1.7657 XPM227 B

AGdWVjRk…LFVsqCnK AFu1q8up…LGS8fQDC

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.

5.585 × 10⁹⁹(100-digit number)

55850187157545255467…18498800451802890239

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

5.585 × 10⁹⁹(100-digit number)

55850187157545255467…18498800451802890239

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.585 × 10⁹⁹(100-digit number)

55850187157545255467…18498800451802890241

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

1.117 × 10¹⁰⁰(101-digit number)

11170037431509051093…36997600903605780479

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.117 × 10¹⁰⁰(101-digit number)

11170037431509051093…36997600903605780481

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

2.234 × 10¹⁰⁰(101-digit number)

22340074863018102187…73995201807211560959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.234 × 10¹⁰⁰(101-digit number)

22340074863018102187…73995201807211560961

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

4.468 × 10¹⁰⁰(101-digit number)

44680149726036204374…47990403614423121919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.468 × 10¹⁰⁰(101-digit number)

44680149726036204374…47990403614423121921

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

8.936 × 10¹⁰⁰(101-digit number)

89360299452072408748…95980807228846243839

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.936 × 10¹⁰⁰(101-digit number)

89360299452072408748…95980807228846243841

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 #536,327

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