Block #674,606

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 8/12/2014, 9:43:49 AM · Difficulty 10.9651 · 6,132,022 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

fddc9983db0ff1fb617c8f15d81f8cbcf8f863519b105eb9b040de35db6e5ea1

View on Chainz ↗

Height

#674,606

Difficulty

10.965128

Transactions

Size

2.88 KB

Version

Bits

0af712a8

Nonce

39,614,730

Timestamp

8/12/2014, 9:43:49 AM

Confirmations

6,132,022

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

b1b3bb7bbe3779b866fabe5bfe529aad9320e342c3d8171d7ceb4b98993c174c

Transactions (2)

Coinbase9f838a3c0cbcea…5c776251aa4ed4

1 in → 1 out8.3800 XPM116 B

ANSXnLY2…Sd25TjkD

59383f8bc037ea…2c5e3fa70d3b39

18 in → 2 out1200.6368 XPM2.68 KB

Ae5PVSvm…TxTzicAX AYZup6GL…HV8PRzkp

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.

1.327 × 10⁹⁸(99-digit number)

13270702996391980799…03571082339231621119

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

1.327 × 10⁹⁸(99-digit number)

13270702996391980799…03571082339231621119

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.327 × 10⁹⁸(99-digit number)

13270702996391980799…03571082339231621121

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

2.654 × 10⁹⁸(99-digit number)

26541405992783961599…07142164678463242239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.654 × 10⁹⁸(99-digit number)

26541405992783961599…07142164678463242241

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

5.308 × 10⁹⁸(99-digit number)

53082811985567923199…14284329356926484479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.308 × 10⁹⁸(99-digit number)

53082811985567923199…14284329356926484481

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

1.061 × 10⁹⁹(100-digit number)

10616562397113584639…28568658713852968959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.061 × 10⁹⁹(100-digit number)

10616562397113584639…28568658713852968961

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

2.123 × 10⁹⁹(100-digit number)

21233124794227169279…57137317427705937919

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.123 × 10⁹⁹(100-digit number)

21233124794227169279…57137317427705937921

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 #674,606

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