Block #569,622

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/31/2014, 6:35:54 AM · Difficulty 10.9648 · 6,224,585 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

261ccd816f90c319fb47820e33f420652bf813a1875e3f0d9fe996dbb669fe8b

View on Chainz ↗

Height

#569,622

Difficulty

10.964783

Transactions

Size

1.24 KB

Version

Bits

0af6fc0a

Nonce

122,227

Timestamp

5/31/2014, 6:35:54 AM

Confirmations

6,224,585

Merkle Root

f8561eefdc6b7e63b8df7ce37a900408c9a02e2ffb6d010f7ee8ee6061239a67

Transactions (4)

Coinbase9bfbc5d739826e…6dda9669b0ddde

1 in → 13 out8.2996 XPM505 B

AQvZBsUo…hppgRZTJ AJzWx2VD…j4ZSMit5 AJtNW28X…Syb4Ph5j AdxPNkWD…ZMa9u34q AQyr8Lw3…hs4nt3Pn

222d3004501c58…27b16776ff280b

1 in → 2 out4.6157 XPM225 B

AYf7i1A3…Fr8quAtN AGdWVjRk…LFVsqCnK

906b9d0759ef89…babebceff985d4

1 in → 2 out1.1064 XPM225 B

AcVexCzF…SY75pd2v AUsphShC…71mN9jj6

0b5da2a0a7c0bd…57a039dcd9d428

1 in → 2 out2.7499 XPM227 B

AewGasuv…7CEsmomB AaYiG7pY…vffN3ach

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.

1.965 × 10¹⁰⁰(101-digit number)

19656520341397349961…05802207983892227839

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

1.965 × 10¹⁰⁰(101-digit number)

19656520341397349961…05802207983892227839

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.965 × 10¹⁰⁰(101-digit number)

19656520341397349961…05802207983892227841

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

3.931 × 10¹⁰⁰(101-digit number)

39313040682794699923…11604415967784455679

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.931 × 10¹⁰⁰(101-digit number)

39313040682794699923…11604415967784455681

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

7.862 × 10¹⁰⁰(101-digit number)

78626081365589399847…23208831935568911359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.862 × 10¹⁰⁰(101-digit number)

78626081365589399847…23208831935568911361

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

1.572 × 10¹⁰¹(102-digit number)

15725216273117879969…46417663871137822719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.572 × 10¹⁰¹(102-digit number)

15725216273117879969…46417663871137822721

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

3.145 × 10¹⁰¹(102-digit number)

31450432546235759939…92835327742275645439

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.145 × 10¹⁰¹(102-digit number)

31450432546235759939…92835327742275645441

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

6.290 × 10¹⁰¹(102-digit number)

62900865092471519878…85670655484551290879

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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