Block #808,925

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 11/13/2014, 5:33:34 AM · Difficulty 10.9735 · 6,001,186 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e8f39c683c1154789fb24d5fd7dafacc92f282b33a8ff18317bcfc169e70abed

View on Chainz ↗

Height

#808,925

Difficulty

10.973522

Transactions

Size

885 B

Version

Bits

0af938bc

Nonce

142,987,737

Timestamp

11/13/2014, 5:33:34 AM

Confirmations

6,001,186

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

63ebbd2d9adec022cfe44dca0fb706463d7befc20bfbb402ba9e3b290f1fecc6

Transactions (4)

Coinbasea9c4187f3be580…3d41eda63cfe55

1 in → 1 out8.3200 XPM116 B

ANSXnLY2…Sd25TjkD

5ba63d60680832…02107f689568a8

1 in → 2 out28801.3511 XPM226 B

AesRMui3…Nhroyfkv AZKMs3V4…ZkVqYFMy

92c642b4455ef9…65f7f83fcf018c

1 in → 2 out4.2700 XPM226 B

AY3DQwTV…DHDeeZGk AYbFktBQ…QWLppM9B

a03c9e9ba95f5b…93de4aab47eb80

1 in → 2 out4.2700 XPM226 B

AV7rt6C9…S8tPgqds ATyvURjG…mLKEkqmS

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.

1.089 × 10⁹⁶(97-digit number)

10898791194694590988…94065107285322495999

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

1.089 × 10⁹⁶(97-digit number)

10898791194694590988…94065107285322495999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.089 × 10⁹⁶(97-digit number)

10898791194694590988…94065107285322496001

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

2.179 × 10⁹⁶(97-digit number)

21797582389389181976…88130214570644991999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.179 × 10⁹⁶(97-digit number)

21797582389389181976…88130214570644992001

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

4.359 × 10⁹⁶(97-digit number)

43595164778778363953…76260429141289983999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.359 × 10⁹⁶(97-digit number)

43595164778778363953…76260429141289984001

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

8.719 × 10⁹⁶(97-digit number)

87190329557556727906…52520858282579967999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.719 × 10⁹⁶(97-digit number)

87190329557556727906…52520858282579968001

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

1.743 × 10⁹⁷(98-digit number)

17438065911511345581…05041716565159935999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.743 × 10⁹⁷(98-digit number)

17438065911511345581…05041716565159936001

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

3.487 × 10⁹⁷(98-digit number)

34876131823022691162…10083433130319871999

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 #808,925

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