Block #61,760

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/18/2013, 3:14:19 PM · Difficulty 8.9742 · 6,749,020 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

582a843bf4db8e5402b2ecaa57755e12ebd753b8fac04eaf409b0fca9f3b986c

View on Chainz ↗

Height

#61,760

Difficulty

8.974247

Transactions

Size

1.69 KB

Version

Bits

08f9683c

Nonce

325

Timestamp

7/18/2013, 3:14:19 PM

Confirmations

6,749,020

Mined by

⛏️ P2SHAQxFiRJvwYTRmufPEyRhsT1sRYYk8FwYZ8

Merkle Root

e1e0c5a41b1ec738d722374f3a5a3dae8daba8e9f453c5466c2db508a35ea0fd

Transactions (3)

Coinbasee1672d7458a6d6…1a99ee3e544e88

1 in → 1 out12.4300 XPM110 B

AQxFiRJv…Yk8FwYZ8

affe16d55c4489…d1391e603ff18f

11 in → 1 out200.0000 XPM1.27 KB

AYAQu6v9…Huu7nZAE

cb566ac10bc906…a3fd574ca60206

1 in → 2 out38.3700 XPM226 B

AW1MVK1w…2aFoEwhz Ad8W1UNN…QGAoMZUp

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.

5.193 × 10⁹⁷(98-digit number)

51937917130622053447…45226657047550489169

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

5.193 × 10⁹⁷(98-digit number)

51937917130622053447…45226657047550489169

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.193 × 10⁹⁷(98-digit number)

51937917130622053447…45226657047550489171

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

1.038 × 10⁹⁸(99-digit number)

10387583426124410689…90453314095100978339

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.038 × 10⁹⁸(99-digit number)

10387583426124410689…90453314095100978341

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

2.077 × 10⁹⁸(99-digit number)

20775166852248821378…80906628190201956679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.077 × 10⁹⁸(99-digit number)

20775166852248821378…80906628190201956681

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

4.155 × 10⁹⁸(99-digit number)

41550333704497642757…61813256380403913359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.155 × 10⁹⁸(99-digit number)

41550333704497642757…61813256380403913361

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

8.310 × 10⁹⁸(99-digit number)

83100667408995285515…23626512760807826719

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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 #61,760

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