Block #561,737

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/25/2014, 4:57:06 PM · Difficulty 10.9655 · 6,248,473 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8e09bf181d4a12f511ef7077103f070e67b90fb3a134e6d2db376272180e5d19

View on Chainz ↗

Height

#561,737

Difficulty

10.965451

Transactions

Size

886 B

Version

Bits

0af727d2

Nonce

1,302,803,049

Timestamp

5/25/2014, 4:57:06 PM

Confirmations

6,248,473

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

46c50c147be191cd681d806e342b763174b48be790718586c74ffd11a05e3dc8

Transactions (4)

Coinbase5b2564df1b7e59…beafae06b0df61

1 in → 1 out8.3300 XPM116 B

ANSXnLY2…Sd25TjkD

7e8d7f4531b9c5…032b4abef309b2

1 in → 2 out6.2057 XPM225 B

AaXAQfWk…hkUAqA84 AdUG8ZY8…Mm3pzFAN

fe48aec048e6f6…8045ea8de3def2

1 in → 2 out1.4426 XPM226 B

ANQcLuxb…h5eS9Jmr AMv4b5jh…t5aAEb3e

7b1bc3901863db…03ad67849518d8

1 in → 2 out5.5648 XPM227 B

AMFnWCdG…H3DCR8Zd AceSi4nc…MdXFen4r

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.

6.331 × 10⁹⁸(99-digit number)

63317927794064316999…09967005603687973119

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

6.331 × 10⁹⁸(99-digit number)

63317927794064316999…09967005603687973119

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.331 × 10⁹⁸(99-digit number)

63317927794064316999…09967005603687973121

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

1.266 × 10⁹⁹(100-digit number)

12663585558812863399…19934011207375946239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.266 × 10⁹⁹(100-digit number)

12663585558812863399…19934011207375946241

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

2.532 × 10⁹⁹(100-digit number)

25327171117625726799…39868022414751892479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.532 × 10⁹⁹(100-digit number)

25327171117625726799…39868022414751892481

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

5.065 × 10⁹⁹(100-digit number)

50654342235251453599…79736044829503784959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.065 × 10⁹⁹(100-digit number)

50654342235251453599…79736044829503784961

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

1.013 × 10¹⁰⁰(101-digit number)

10130868447050290719…59472089659007569919

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.013 × 10¹⁰⁰(101-digit number)

10130868447050290719…59472089659007569921

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 #561,737

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