Block #695,566

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 8/27/2014, 4:47:43 PM · Difficulty 10.9577 · 6,113,235 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

67fe3249864e53f55db1f7bf01d4566272ff2800200b380b4e2b4e323a70f75f

View on Chainz ↗

Height

#695,566

Difficulty

10.957717

Transactions

Size

664 B

Version

Bits

0af52ced

Nonce

554,596

Timestamp

8/27/2014, 4:47:43 PM

Confirmations

6,113,235

Mined by

⛏️ aSIAJzWx2VDShfKP9pKK3jZqTbn4sj4ZSMit5

Merkle Root

519774c0e3c993d4f3291456ac3ed6ba2cd27134bdd6df7ff0e6af5df6e7c046

Transactions (1)

Coinbase519774c0e3c993…e6af5df6e7c046

1 in → 15 out8.3200 XPM573 B

AJzWx2VD…j4ZSMit5 AdRccEFQ…6E9x7zBA AUH8MTP4…tSSjzeSq AebWhrRm…K61Qrkws AXz2kWvX…V5ZFCDBd

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.

4.490 × 10⁹⁷(98-digit number)

44904048164728563147…87310367836892041759

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

4.490 × 10⁹⁷(98-digit number)

44904048164728563147…87310367836892041759

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.490 × 10⁹⁷(98-digit number)

44904048164728563147…87310367836892041761

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

8.980 × 10⁹⁷(98-digit number)

89808096329457126295…74620735673784083519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.980 × 10⁹⁷(98-digit number)

89808096329457126295…74620735673784083521

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

1.796 × 10⁹⁸(99-digit number)

17961619265891425259…49241471347568167039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.796 × 10⁹⁸(99-digit number)

17961619265891425259…49241471347568167041

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

3.592 × 10⁹⁸(99-digit number)

35923238531782850518…98482942695136334079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.592 × 10⁹⁸(99-digit number)

35923238531782850518…98482942695136334081

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

7.184 × 10⁹⁸(99-digit number)

71846477063565701036…96965885390272668159

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.184 × 10⁹⁸(99-digit number)

71846477063565701036…96965885390272668161

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

1.436 × 10⁹⁹(100-digit number)

14369295412713140207…93931770780545336319

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 #695,566

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