Block #561,261

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/25/2014, 9:56:05 AM · Difficulty 10.9651 · 6,283,628 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

4c02f206d8fb4090c70b98ad5e81334d1f590d3f5878cf8030652580cd976fda

View on Chainz ↗

Height

#561,261

Difficulty

10.965054

Transactions

Size

1.09 KB

Version

Bits

0af70dc5

Nonce

112,435,564

Timestamp

5/25/2014, 9:56:05 AM

Confirmations

6,283,628

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

adb8e53710e8c089eb9554d499b132d710efbe669242552bd27e005853b90e15

Transactions (5)

Coinbase48355b20935e8f…aee52ab53d7b0a

1 in → 1 out8.3400 XPM116 B

ANSXnLY2…Sd25TjkD

34d35b410c62b9…218a5b1eb8f4c8

1 in → 2 out7.6758 XPM227 B

ANfn3HZ2…2jtoi8UL AMLssXBN…VZyLLL9Z

f8f1bfa618a3b1…3818f07ddabf81

1 in → 2 out1.5068 XPM226 B

AG8u7ddV…cU5QJSqk AehqDn8J…4R6VHaZu

8d3fc05e188dbe…49f4f764c46155

1 in → 2 out7.1402 XPM227 B

AaG6Ks4Q…EDbQR7vJ ATzMcyyx…evMXNRtc

2108cc4e5df2e8…78127eadc0046f

1 in → 2 out5.2604 XPM227 B

AHd5XPWp…R1L25agP AWYfjpEz…riFRNoLs

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.

1.267 × 10⁹⁹(100-digit number)

12671031754434948998…76972984741868868799

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

1.267 × 10⁹⁹(100-digit number)

12671031754434948998…76972984741868868799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.267 × 10⁹⁹(100-digit number)

12671031754434948998…76972984741868868801

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

2.534 × 10⁹⁹(100-digit number)

25342063508869897997…53945969483737737599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.534 × 10⁹⁹(100-digit number)

25342063508869897997…53945969483737737601

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

5.068 × 10⁹⁹(100-digit number)

50684127017739795994…07891938967475475199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.068 × 10⁹⁹(100-digit number)

50684127017739795994…07891938967475475201

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

1.013 × 10¹⁰⁰(101-digit number)

10136825403547959198…15783877934950950399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.013 × 10¹⁰⁰(101-digit number)

10136825403547959198…15783877934950950401

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

2.027 × 10¹⁰⁰(101-digit number)

20273650807095918397…31567755869901900799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.027 × 10¹⁰⁰(101-digit number)

20273650807095918397…31567755869901900801

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 #561,261

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