Block #672,074

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 8/10/2014, 4:59:06 PM · Difficulty 10.9644 · 6,161,172 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e7dca4acefd94bb92989004340df5a622cea4ee65eeb7819f95634376a32623f

View on Chainz ↗

Height

#672,074

Difficulty

10.964441

Transactions

Size

2.02 KB

Version

Bits

0af6e5a1

Nonce

10,827,086

Timestamp

8/10/2014, 4:59:06 PM

Confirmations

6,161,172

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

67139b0c9a31fd462723b5806bf20af0fbe0ed0f3be376dcfb7caadf00f37aac

Transactions (4)

Coinbase75d035110d78f4…e4ab0dedf4e56e

1 in → 1 out8.3400 XPM116 B

ANSXnLY2…Sd25TjkD

cf2eb721a6a043…70fb931b7c8250

1 in → 2 out6.5484 XPM226 B

AKALqk9A…SvkQXitC AQ4S8AtJ…Hzkvi1gQ

a35fa584ee2c12…6bd1b103b93289

2 in → 2 out3.9491 XPM375 B

ANLSpbra…aYZnuDth AG5hxwUv…PHoetpdt

b0d8524bbd92a6…7e11945182ea0c

8 in → 2 out5.1872 XPM1.23 KB

ATUJFkEF…j71DTZhm AboYmx4z…u4VqqakG

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.

4.937 × 10⁹⁸(99-digit number)

49371269246830012473…53922159072700334079

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

4.937 × 10⁹⁸(99-digit number)

49371269246830012473…53922159072700334079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.937 × 10⁹⁸(99-digit number)

49371269246830012473…53922159072700334081

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

9.874 × 10⁹⁸(99-digit number)

98742538493660024946…07844318145400668159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.874 × 10⁹⁸(99-digit number)

98742538493660024946…07844318145400668161

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

1.974 × 10⁹⁹(100-digit number)

19748507698732004989…15688636290801336319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.974 × 10⁹⁹(100-digit number)

19748507698732004989…15688636290801336321

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

3.949 × 10⁹⁹(100-digit number)

39497015397464009978…31377272581602672639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.949 × 10⁹⁹(100-digit number)

39497015397464009978…31377272581602672641

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

7.899 × 10⁹⁹(100-digit number)

78994030794928019957…62754545163205345279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.899 × 10⁹⁹(100-digit number)

78994030794928019957…62754545163205345281

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

1.579 × 10¹⁰⁰(101-digit number)

15798806158985603991…25509090326410690559

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

Block #672,074

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